Skip to main content Accessibility help
×
Hostname: page-component-78c5997874-fbnjt Total loading time: 0 Render date: 2024-11-17T23:21:12.761Z Has data issue: false hasContentIssue false

Bibliography

Published online by Cambridge University Press:  05 June 2014

R. M. Dudley
Affiliation:
Massachusetts Institute of Technology
Get access
Type
Chapter
Information
Publisher: Cambridge University Press
Print publication year: 2014

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Alexander, Kenneth S. (1984). Probability inequalities for empirical processes and a law of the iterated logarithm. Ann. Probab. 12, 1041–1067.CrossRefGoogle Scholar
Alexander, K. S. (1987). The central limit theorem for empirical processes on Vapnik-Červonenkis classes. Ann. Probab. 15, 178–203.CrossRefGoogle Scholar
Alon, N., Ben-David, S., Cesa-Bianchi, N., and Haussler, D. (1997) Scale-sensitive dimensions, uniform convergence, and learnability. J. ACM 44, 615–663.CrossRefGoogle Scholar
Andersen, Niels Trolle (1985a). The central limit theorem for non–separable valued functions. Z. Wahrsch. verw. Gebiete 70, 445–455.CrossRefGoogle Scholar
Andersen, N. T. (1985b). The calculus of non-measurable functions and sets. Various Publ. Ser. no. 36, Matematisk Institut, Aarhus Universitet.Google Scholar
Andersen, N. T., and Dobrić, Vladimir (1987). The central limit theorem for stochastic processes. Ann. Probab. 15, 164–177.CrossRefGoogle Scholar
Andersen, N. T., and Dobrić, V. (1988). The central limit theorem for stochastic processes II. J. Theoret. Probab. 1, 287–303.CrossRefGoogle Scholar
Andersen, N. T., Gine, E., Ossiander, M., and Zinn, J. (1988). The central limit theorem and the law of the iterated logarithm for empirical processes under local conditions. Probab. Theory Related Fields 77, 271–305.CrossRefGoogle Scholar
Anderson, Theodore W. (1955). The integral of a symmetric unimodal function over a symmetric convex set and some probability inequalities. Proc. Amer. Math. Soc. 6, 170–176.CrossRefGoogle Scholar
Araujo, Aloisio, and Giné, E. (1980). The Central Limit Theorem for Real and Banach Valued Random Variables. Wiley, New York.Google Scholar
Arcones, Miguel A., and Giné, E. (1993). Limit theorems for U-processes. Ann. Probab. 21, 1494–1542.CrossRefGoogle Scholar
Assouad, Patrice (1981). Sur les classes de Vapnik-Červonenkis. C. R. Acad. Sci. Paris Sér. I 292, 921–924.Google Scholar
Assouad, P. (1982). Classes de Vapnik–Červonenkis et vitesse d'estimation (unpublished manuscript).Google Scholar
Assouad, P. (1983). Densité et dimension. Ann. Inst. Fourier (Grenoble) 33, no. 3, 233–282.CrossRefGoogle Scholar
Assouad, P. (1985). Observations sur les classes de Vapnik–Červonenkis et la dimension combinatoire de Blei. In Séminaire d'analyse harmonique, 1983–84, Publ. Math. Orsay, Univ. Paris XI, Orsay, 92–112.Google Scholar
Assouad, P., and Dudley, R. M. (1990). Minimax nonparametric estimation over classes of sets (unpublished manuscript).Google Scholar
Aumann, Robert J. (1961). Borel structures for function spaces. Illinois J. Math. 5, 614–630.Google Scholar
Bahadur, Raghu Raj (1954). Sufficiency and statistical decision functions. Ann. Math. Statist. 25, 423–462.CrossRefGoogle Scholar
Bakel'man, I. Ya. (1965). Geometric Methods of Solution of Elliptic Equations (in Russian). Nauka, Moscow.Google Scholar
Bakhvalov, N. S. (1959). On approximate calculation of multiple integrals. Vestnik Moskov. Univ. Ser. Mat. Mekh. Astron. Fiz. Khim. 1959, No. 4, 3–18.Google Scholar
Bauer, Heinz (1981). Probability Theory and Elements of Measure Theory, 2nd ed. Academic Press, London.Google Scholar
Bennett, George W. (1962). Probability inequalities for the sum of bounded random variables. J. Amer. Statist. Assoc. 57, 33–15.CrossRefGoogle Scholar
Berkes, István, and Philipp, Walter (1977). An almost sure invariance principle for the empirical distribution function of mixing random variables. Z. Wahrsch. verw. Gebiete 41, 115–137.CrossRefGoogle Scholar
Bernštein, Sergei N. (1924). Ob odnom vidoizmenenii neravenstva Chebysheva i o pogreshnosti formuly Laplasa (in Russian). Uchen. Zapiski Nauchn.-issled. Kafedr Ukrainy, Otdel. Mat., vyp. 1, 38–48; reprinted in S. N. Bernštein, Sobranie Sochinenit [Collected Works], Tom IV, Teoriya Veroiatnostei, Matematicheskaya Statistika, Nauka, Moscow, 1964, pp. 71–79.Google Scholar
*Bernštein, S. N. (1927). Teoriya Veroiatnostei (Theory of Probability, in Russian). Moscow. 2nd ed., 1934.Google Scholar
Bickel, Peter J., and Doksum, Kjell A. (2001). Mathematical Statistics, 2nd ed., vol. 1. Prentice–Hall, New York.Google Scholar
Bickel, P. J., and Freedman, David A. (1981). Some asymptotic theory for the bootstrap. Ann. Statist. 9, 1196–1217.CrossRefGoogle Scholar
Billingsley, Patrick (1968). Convergence of Probability Measures. Wiley, New York.Google Scholar
Birkhoff, Garrett (1935). Integration of functions with values in a Banach space. Trans. Amer. Math. Soc. 38, 357–378.Google Scholar
Birnbaum, Zygmunt W., and Orlicz, W. (1931). Über die Verallgemeinerung des Begriffes der zueinander konjugierten Potenzen. Studia Math. 3, 1–67.CrossRefGoogle Scholar
Birnbaum, Z. W., and Tingey, F. H. (1951). One-sided confidence contours for probability distribution functions. Ann. Math. Statist. 22, 592–596.CrossRefGoogle Scholar
Blum, J. R. (1955). On the convergence of empiric distribution functions. Ann. Math. Statist. 26, 527–529.CrossRefGoogle Scholar
Blumberg, Henry (1935). The measurable boundaries of an arbitrary function. Acta Math. (Sweden) 65, 263–282.CrossRefGoogle Scholar
Bochner, Salomon (1933). Integration von Funktionen, deren Werte die Elemente eines Vektorraumes sind. Fund. Math. 20, 262–276.CrossRefGoogle Scholar
Bolthausen, Erwin (1978). Weak convergence of an empirical process indexed by the closed convex subsets of I2. Z. Wahrsch. verw. Gebiete 43, 173–181.CrossRefGoogle Scholar
Bonnesen, Tommy, and Fenchel, Werner (1934). Theorie der konvexen Körper. Berlin, Springer; repr. Chelsea, New York, 1948.CrossRefGoogle Scholar
Borell, Christer (1974). Convex measures on locally convex spaces. Ark. Mat. 12, 239–252.CrossRefGoogle Scholar
Borell, C. (1975a). Convex set functions in d-space. Period. Math. Hungar. 6, 111–136.CrossRefGoogle Scholar
Borell, C. (1975b). The Brunn–Minkowski inequality in Gauss space. Invent. Math. 30, 207–216.CrossRefGoogle Scholar
Borisov, Igor S. (1981). Some limit theorems for empirical distributions (in Russian). Abstracts of Reports, Third Vilnius Conf. Probability Th. Math. Statist. 1, 71–72.Google Scholar
Bousquet, O., Koltchinskii, V., and Panchenko, D. (2002). Some local measures of complexity of convex hulls and generalization bounds. COLT [Conference on Learning Theory], Lecture Notes on Artificial Intelligence 2375, 59–73.Google Scholar
Bretagnolle, Jean, and Massart, Pascal (1989). Hungarian constructions from the nonasymptotic viewpoint. Ann. Probab. 17, 239–256.CrossRefGoogle Scholar
Bronshtein [Bronštein], E. M. (1976). ∈-entropy of convex sets and functions. Siberian Math. J. 17, 393–398, transl. from Sibirsk. Mat. Zh. 17, 508–514.Google Scholar
Brown, Lawrence D. (1986). Fundamentals of Statistical Exponential Families, Inst. Math. Statist. Lecture Notes–Monograph Ser. 9, Hayward, CA.Google Scholar
Cantelli, Francesco Paolo (1933). Sulla determinazione empirica della leggi di probabilità. Giorn. Ist. Ital. Attuari 4, 421–424.Google Scholar
Carl, Bernd (1982). On a characterization of operators from lq into a Banach space of type p with some applications to eigenvalue problems. J. Funct. Anal. 48, 394–407.CrossRefGoogle Scholar
Carl, B. (1997). Metric entropy of convex hulls in Hilbert space. Bull. London Math. Soc. 29, 452–458.CrossRefGoogle Scholar
Chernoff, Herman (1952). A measure of asymptotic efficiency for tests of a hypothesis based on the sum of observations. Ann. Math. Statist. 23, 493–507.CrossRefGoogle Scholar
Chevet, Simone (1970). Mesures de Radon sur ℝn et mesures cylindriques. Ann. Fac. Sci. Univ. Clermont #43 (math., 6° fasc.), 91–158.Google Scholar
Clements, G. F. (1963). Entropies of several sets of real valued functions. Pacific J. Math 13, 1085–1095.CrossRefGoogle Scholar
Coffman, E. G. Jr., and Lueker, George S. (1991). Probabilistic Analysis of Packing and Partitioning Algorithms.Wiley, New York.Google Scholar
Coffman, E. G., and Shor, Peter W. (1991). A simple proof of the upright matching bound. SIAM J. Discrete Math. 4, 48–57.CrossRefGoogle Scholar
Cohn, Donald L. (1980). Measure Theory. Birkhäuser, Boston. (Second Ed., 2013.)CrossRefGoogle Scholar
Cover, Thomas M. (1965). Geometric and statistical properties of systems of linear inequalities with applications to pattern recognition. IEEE Trans. Elec. Comp. EC-14 326–334.CrossRefGoogle Scholar
*Csáki, E. (1974). Investigations concerning the empirical distribution function. Magyar Tud. Akad. Mat. Fiz. Oszt. Kozl. 23 239–327; English transl. in Selected Transl. Math. Statist. Probab. 15 (1981), 229–317.Google Scholar
Csörgő, Miklós, and Horváth, Lajos (1993). Weighted Approximations in Probability and Statistics. Wiley, Chichester.Google Scholar
Csörgő, M., and Révész, Pal (1981). Strong Approximations in Probability and Statistics. Academic, New York.Google Scholar
Cuesta, J. A., and Matrán, C. (1989). Notes on the Wasserstein metric in Hilbert spaces. Ann. Probab. 17, 1264–1276.CrossRefGoogle Scholar
Danzer, Ludwig, Grünbaum, Branko, and Klee, Victor L. (1963). Helly's theorem and its relatives. Proc. Symp. Pure Math. (Amer. Math. Soc.) 7, 101–180.Google Scholar
Darmois, Georges (1951). Sur une propriété caractéristique de la loi de probabilité de Laplace. Comptes Rendus Acad. Sci. Paris 232, 1999–2000.Google Scholar
Darst, Richard B. (1971). C∞ functions need not be bimeasurable. Proc. Amer. Math. Soc. 27, 128–132.Google Scholar
Davis, Philip J., and Polonsky, Ivan (1972). Numerical interpolation, differentiation and integration. Chapter 25 in Handbook of Mathematical Functions, ed. M., Abramowitz and I. A., Stegun, Dover, New York, 9th printing.Google Scholar
DeHardt, John (1971). Generalizations of the Glivenko–Cantelli theorem. Ann. Math. Statist. 42, 2050–2055.CrossRefGoogle Scholar
*Dobrushin, R. L. (1970). Prescribing a system of random variables by conditional distributions. Theory Probab. Appl. 15, 458–186.CrossRefGoogle Scholar
Donsker, M. D. (1952). Justification and extension of Doob's heuristic approach to the Kolmogorov–Smirnov theorems. Ann. Math. Statist. 23, 277–281.CrossRefGoogle Scholar
Doob, Joseph L. (1949). Heuristic approach to the Kolmogorov–Smirnov theorems. Ann. Math. Statist. 20, 393–403.CrossRefGoogle Scholar
Drake, Frank R. (1974). Set Theory: An Introduction to Large Cardinals. North-Holland, Amsterdam.Google Scholar
Dudley, R. M. (1966). Weak convergence of probabilities on nonseparable metric spaces and empirical measures on Euclidean spaces. Illinois J. Math. 10, 109–126.Google Scholar
Dudley, R. M. (1967a). The sizes of compact subsets of Hilbert space and continuity of Gaussian processes. J. Funct. Anal. 1, 290–330.CrossRefGoogle Scholar
Dudley, R. M. (1967b). Measures on non-separable metric spaces. Illinois J. Math. 11, 449–453.Google Scholar
Dudley, R. M. (1968). Distances of probability measures and random variables. Ann. Math. Statist. 39, 1563–1572.CrossRefGoogle Scholar
Dudley, R. M. (1973). Sample functions of the Gaussian process. Ann. Probab. 1, 66–103.CrossRefGoogle Scholar
Dudley, R. M. (1974). Metric entropy of some classes of sets with differentiable boundaries. J. Approx. Theory 10, 227–236; Correction 26 (1979), 192–193.CrossRefGoogle Scholar
Dudley, R. M. (1978). Central limit theorems for empirical measures. Ann. Probab. 6, 899–929; Correction 7 (1979), 909–911.CrossRefGoogle Scholar
Dudley, R. M. (1980). Acknowledgment of priority: Second derivatives of convex functions. Math. Scand. 46, 61.CrossRefGoogle Scholar
Dudley, R. M. (1981). Donsker classes of functions. In Statistics and Related Topics (Proc. Symp. Ottawa, 1980), North-Holland, New York, 341–352.Google Scholar
Dudley, R. M. (1982). Empirical and Poisson processes on classes of sets or functions too large for central limit theorems. Z. Wahrsch. verw. Gebiete 61, 355–368.CrossRefGoogle Scholar
Dudley, R. M. (1984). A course on empirical processes. Ecole d'été de probabilités de St.-Flour, 1982. Lecture Notes in Math. (Springer) 1097, 1–142.Google Scholar
Dudley, R. M. (1985a). An extended Wichura theorem, definitions of Donsker class, and weighted empirical distributions. In Probability in Banach Spaces V (Proc. Conf. Medford, 1984), Lecture Notes in Math. (Springer) 1153, 141–178.Google Scholar
Dudley, R. M. (1985b). The structure of some Vapnik–Červonenkis classes. In Proc. Berkeley Conf. in Honor of J. Neyman and J. Kiefer 2, 495–508. Wadsworth, Belmont, CA.Google Scholar
Dudley, R. M. (1987). Universal Donsker classes and metric entropy. Ann. Probab. 15, 1306–1326.CrossRefGoogle Scholar
Dudley, R. M. (1990). Nonlinear functionals of empirical measures and the bootstrap. In Probability in Banach Spaces 7, Proc. Conf. Oberwolfach, 1988, Progress in Probability 21, Birkhäuser, Boston, 63–82.Google Scholar
Dudley, R. M. (1994). Metric marginal problems for set-valued or non-measurable variables. Probab. Theory Related Fields 100, 175–189.CrossRefGoogle Scholar
Dudley, R. M. (2000). Notes on Empirical Processes. MaPhySto Lecture Notes 4, Aarhus, Denmark.Google Scholar
Dudley, R. M. (2002). Real Analysis and Probability. 2nd ed., Cambridge University Press, Cambridge.CrossRefGoogle Scholar
Dudley, R. M., Giné, E., and Zinn, J. (1991). Uniform and universal Glivenko–Cantelli classes. J. Theoret. Probab. 4, 485–210.CrossRefGoogle Scholar
Dudley, R. M., and Koltchinskii, V. I. (1994, 1996). Envelope moment conditions and Donsker classes. Theory Probab. Math. Statist. No. 51, 39–18; Ukrainian version, Teor. Ĭmovĭr. Mat. Stat. No. 51 (1994) 39–49.Google Scholar
Dudley, R. M., Kulkarni, S. R., Richardson, T., and Zeitouni, O. (1994). A metric entropy bound is not sufficient for learnability. IEEE Trans. Inform. Theory 40, 883–885.CrossRefGoogle Scholar
Dudley, R. M., and Philipp, Walter (1983). Invariance principles for sums of Banach space valued random elements and empirical processes. Z. Wahrsch. verw. Gebiete 62, 509–552.CrossRefGoogle Scholar
Dunford, Nelson (1936). Integration and linear operations. Trans. Amer. Math. Soc. 40, 474–494.CrossRefGoogle Scholar
Dunford, N., and Schwartz, Jacob T. (1958). Linear Operators. Part I: General Theory. Interscience, New York. Repr. 1988.Google Scholar
Durst, Mark, and Dudley, R. M. (1981). Empirical processes, Vapnik–Chervonenkis classes and Poisson processes. Probab. Math. Statist. (Wrocław) 1, no. 2, 109–115.Google Scholar
Dvoretzky, A., Kiefer, J., and Wolfowitz, J. (1956). Asymptotic minimax character of the sample distribution function and the classical multinomial estimator. Ann. Math. Statist. 27, 642–669.CrossRefGoogle Scholar
Eames, W., and May, L. E. (1967). Measurable cover functions. Canad. Math. Bull. 10, 519–523.CrossRefGoogle Scholar
Effros, Edward G. (1965). Convergence of closed subsets in a topological space. Proc. Amer. Math. Soc. 16, 929–931.CrossRefGoogle Scholar
Efron, Bradley (1979). Bootstrap methods: another look at the jackknife. Ann. Statist. 7, 1–26.CrossRefGoogle Scholar
Efron, B., and Tibshirani, Robert J. (1993). An Introduction to the Bootstrap. Chapman and Hall, New York.CrossRefGoogle Scholar
Eggleston, H. G. (1958). Convexity. Cambridge University Press, Cambridge. Reprinted with corrections, 1969.CrossRefGoogle Scholar
Eilenberg, Samuel, and Steenrod, Norman (1952). Foundations of Algebraic Topology. Princeton University Press, Princeton, NJ.CrossRefGoogle Scholar
Eršov, M. P. (1975). The Choquet theorem and stochastic equations. Analysis Math. 1, 259–271.Google Scholar
Evstigneev, I. V. (1977). “Markov times” for random fields. Theory Probab. Appl. 22, 563–569; Teor. Veroiatnost. i Primenen. 22, 575–581.Google Scholar
Feldman, Jacob (1972). Sets of boundedness and continuity for the canonical normal process. Proc. Sixth Berkeley Symposium Math. Statist. Prob. 2, pp. 357–367. University of California Press, Berkeley and Los Angeles.Google Scholar
Feller, William (1968). An Introduction to Probability Theory and Its Applications. Vol. 1, 3rd ed. Wiley, New York.Google Scholar
Feller, W. (1971). An Introduction to Probability Theory and Its Applications. Vol. 2, 2nd ed. Wiley, New York.Google Scholar
Ferguson, Thomas S. (1967). Mathematical Statistics: A Decision Theoretic Approach. Academic Press, New York.Google Scholar
Fernique, Xavier (1964). Continuité des processus gaussiens. Comptes Rendus Acad. Sci. Paris 258, 6058–6060.Google Scholar
Fernique, X. (1970). Intégrabilité des vecteurs gaussiens. Comptes Rendus Acad. Sci. Paris Ser. A 270, 1698–1699.Google Scholar
Fernique, X. (1971). Régularité de processus gaussiens. Invent. Math. 12, 304–320.CrossRefGoogle Scholar
Fernique, X. (1975). Régularité des trajectoires des fonctions aléatoires gaussiennes. Ecole d'ete de probabilites de St.-Flour, 1974. Lecture Notes in Math. (Springer) 480, 1–96.Google Scholar
Fernique, X. (1985). Sur la convergence étroite des mesures gaussiennes. Z. Wahrsch. verw. Gebiete 68, 331–336.CrossRefGoogle Scholar
Fernique, X. (1997). Fonctions aléatoires gaussiennes, vecteurs aléatoires gaussiens. Publications du Centre de Recherches Mathématiques, Montréal.Google Scholar
Fisher, Ronald Aylmer (1922). IX. On the mathematical foundations of theoretical statistics. Phil. Trans. Roy. Soc. London Sér. A 222, 309–368.Google Scholar
Freedman, David A. (1966). On two equivalence relations between measures. Ann. Math. Statist. 37, 686–689.CrossRefGoogle Scholar
Gaenssler, Peter (1986). Bootstrapping empirical measures indexed by Vapnik–Chervonenkis classes of sets. In Probability Theory and Mathematical Statistics (Vilnius, 1985), Yu. V., Prohorov, V. A., Statulevičius, V. V., Sazonov, and B., Grigelionis, eds., VNU Science Press, Utrecht, 467–481.Google Scholar
Gaenssler, P., and Stute, Winfried (1979). Empirical processes: a survey of results for independent and identically distributed random variables. Ann. Probab. 7, 193–243.CrossRefGoogle Scholar
*Gelfand, Izrail' Moiseevich (1936). Sur un lemme de la théorie des espaces linéaires. Communications de l'Institut des Sciences Math. et Mécaniques de l'Université de Kharkoff et de la Societé Math. de Kharkov (= Zapiski Khark. Mat. Obshchestva) (Ser. 4) 13, 35–40.Google Scholar
Gelfand, I. M. (1938). Abstrakte Funktionen und lineare Operatoren. Mat. Sbornik (N. S.) 4, 235–286.Google Scholar
Giné, Evarist (1974). On the central limit theorem for sample continuous processes. Ann. Probab. 2, 629–641.Google Scholar
Giné, E. (1997). Lectures on some aspects of the bootstrap. In Lectures on Probability Theory and Statistics, Ecole d'été de probabilités de Saint-Flour (1996), ed. P., Bernard. Lecture Notes in Math. (Springer) 1665, 37–151.CrossRefGoogle Scholar
Giné, E., and Zinn, Joel (1984). Some limit theorems for empirical processes. Ann. Probab. 12, 929–989.CrossRefGoogle Scholar
Giné, E., and Zinn, J. (1986). Lectures on the central limit theorem for empirical processes. In Probability and Banach Spaces, Proc. Conf. Zaragoza, 1985, Lecture Notes in Math. 1221, 50–113. Springer, Berlin.CrossRefGoogle Scholar
Giné, E. and Zinn, J. (1990). Bootstrapping general empirical measures. Ann. Probab. 18, 851–869.CrossRefGoogle Scholar
Giné, E. and Zinn, J. (1991). Gaussian characterization of uniform Donsker classes of functions. Ann. Probab. 19, 758–782.CrossRefGoogle Scholar
Glivenko, V. I. (1933). Sulla determinazione empirica della leggi di probabilità. Giorn. Ist. Ital. Attuari 4, 92–99.Google Scholar
Gnedenko, B. V., and Kolmogorov, A. N. (1949). Limit Distributions for Sums of Independent Random Variables. Moscow. Transl. and ed. by K. L., Chung, Addison-Wesley, Reading, Mass., 1954, rev. ed. 1968.Google Scholar
Goffman, C., and Zink, R. E. (1960). Concerning the measurable boundaries of a real function. Fund. Math. 48, 105–111.CrossRefGoogle Scholar
Gordon, Yehoram (1985). Some inequalities for Gaussian processes and applications. Israel J. Math. 50, 265–289.CrossRefGoogle Scholar
Graves, L. M. (1927). Riemann integration and Taylor's theorem in general analysis. Trans. Amer. Math. Soc. 29, 163–177.Google Scholar
Gross, Leonard (1962). Measurable functions on Hilbert space. Trans. Amer. Math. Soc. 105, 372–390.CrossRefGoogle Scholar
Gruber, P. M. (1983). Approximation of convex bodies. In Convexity and its Applications, ed. P. M., Gruber and J. M., Wills. Birkhäuser, Basel, pp. 131–162.CrossRefGoogle Scholar
Gutmann, Samuel (1981). Unpublished manuscript.
Hall, Peter (1992). The Bootstrap and Edgeworth Expansion. Springer, New York.CrossRefGoogle Scholar
Halmos, Paul R., and Savage, Leonard Jimmie (1949). Application of the Radon–Nikodym theorem to the theory of sufficient statistics. Ann. Math. Statist. 20, 225–241.CrossRefGoogle Scholar
Harary, F. (1969). Graph Theory. Addison-Wesley, Reading, MA.CrossRefGoogle Scholar
Harding, E. F. (1967). The number of partitions of a set of N points in k dimensions induced by hyperplanes. Proc. Edinburgh Math. Soc. (Ser. II) 15, 285–289.CrossRefGoogle Scholar
Hausdorff, Felix (1914). Mengenlehre, transl. by J. P., Aumann et al. as Set Theory. 3rd English ed. of transl. of 3rd German edition (1937). Chelsea, New York, 1978.Google Scholar
Haussler, D. (1995). Sphere packing mumbers for subsets of the Boolean n-cube with bounded Vapnik–Chervonenkis dimension. J. Combin. Theory Ser. A 69, 217–232.CrossRefGoogle Scholar
Hewitt, Edwin, and Ross, Kenneth A. (1979). Abstract Harmonic Analysis, vol. 1, 2nd ed. Springer, Berlin.Google Scholar
Hobson, E. W. (1926). The Theory of Functions of a Real Variable and the Theory of Fourier's Series, vol. 2, 2nd ed. Repr. Dover, New York, 1957.Google Scholar
Hoeffding, Wassily (1963). Probability inequalities for sums of bounded random variables. J. Amer. Statist. Assoc. 58, 13–30.CrossRefGoogle Scholar
Hoffman, Kenneth (1975). Analysis in Euclidean Space. Prentice-Hall, Englewood Cliffs, NJ.Google Scholar
Hoffmann-Jørgensen, Jørgen (1974). Sums of independent Banach space valued random elements. Studia Math. 52, 159–186.CrossRefGoogle Scholar
Hoffmann-Jørgensen, J. (1984). Stochastic Processes on Polish Spaces. Published (1991): Various Publication Series no. 39, Matematisk Institut, Aarhus Universitet.Google Scholar
Hoffmann-Jørgensen, J. (1985). The law of large numbers for non-measurable and non-separable random elements. Astérisque 131, 299–356.Google Scholar
Hörmander, L. (1983). The Analysis of Linear Partial Differential Operators I. Springer, Berlin.Google Scholar
Hu, Inchi (1985). A uniform bound for the tail probability of Kolmogorov–Smirnov statistics. Ann. Statist. 13, 821–826.CrossRefGoogle Scholar
Il'in, V. A., and Pozniak, E. G. (1982). Fundamentals of Mathematical Analysis. Transl. from the 4th Russian ed. (1980) by V. Shokurov. Mir, Moscow.Google Scholar
Itô, Kiyosi, and McKean, Henry P. Jr. (1974). Diffusion Processes and Their Sample Paths. Springer, Berlin.Google Scholar
Jain, Naresh C., and Marcus, Michael B. (1975). Central limit theorems for C(S)-valued random variables. J. Funct. Anal. 19, 216–231.CrossRefGoogle Scholar
Kac, M. (1949). On deviations between theoretical and empirical distributions. Proc. Nat. Acad. Sci. USA 35, 252–257.CrossRefGoogle ScholarPubMed
Kahane, Jean-Pierre (1985). Some Random Series ofFunctions, 2nd ed. Cambridge University Press, Cambridge.Google Scholar
Kahane, J.-P. (1986). Une inégalité du type de Slepian et Gordon sur les processus gaussiens. Israel J. Math. 55, 109–110.CrossRefGoogle Scholar
*Kantorovich, L. V. (1942). On the transfer of masses. Dokl. AkadNauk. SSSR 37, 7–8.Google Scholar
Kantorovich, L. V., and Rubinshtein, G. Sh. (1958). On a space of completely additive functions. Vestnik Leningrad Univ. 13 no. 7, Ser. Math. Astron. Phys. 2, 52–59 (in Russian).Google Scholar
Kartashev, A. P., and Rozhdestvenskiĭ, B. L. (1984). Matematicheskiĭ Analiz (Mathematical Analysis; in Russian). Nauka, Moscow. French transl.: Kartachev, A., and Rojdestvenski, B.Analyse mathématique, transl. by Djilali Embarek. Mir, Moscow, 1988.Google Scholar
Kelley, John L. (1955). General Topology. Van Nostrand, Princeton, NJ. Repr. Springer, New York, 1975.Google Scholar
Kolmogorov, A. N. (1933a). Über die Grenzwertsätze der Wahrscheinlichkeitsrechnung. Izv. Akad. Nauk SSSR (Bull. Acad. Sci. URSS) (Ser. 7) no. 3, 363–372.Google Scholar
*Kolmogorov, A. N. (1933b). Sulla determinazione empirica di una legge di distribuzione. Giorn. Ist. Ital. Attuari 4, 83–91.Google Scholar
Kolmogorov, A. N. (1955). Bounds for the minimal number of elements of an ε-net in various classes of functions and their applications to the question of representability of functions of several variables by superpositions of functions of fewer variables (in Russian). Uspekhi Mat. Nauk 10, no. 1 (63), 192–194.Google Scholar
Kolmogorov, A. N. (1956). On Skorokhod convergence. Theory Probab. Appl. 1, 215–222.CrossRefGoogle Scholar
Kolmogorov, A. N., and Tikhomirov, V. M. (1959). ε-entropy and ε-capacity of sets in function spaces. Uspekhi Mat. Nauk 14, no. 2, 3–86 = Amer. Math. Soc. Transl. (Serr. 2) 17 (1961), 277–364.Google Scholar
Koltchinskii, Vladimir I. (1981). On the central limit theorem for empirical measures. Theor. Probab. Math. Statist. 24, 71–82. Transl. from Teor. Verojatnost. i Mat. Statist. (1981) 24, 63–75.Google Scholar
*Komatsu, Y. (1955). Elementary inequalities for Mills ratio. Rep. Statist. Appl. Res. Un. Japan. Sci. Engrs. 4, 69–70.Google Scholar
Komlós, János, Major, Péter, and Tusnády, Gábor (1975). An approximation of partial sums of independent RV'-s and the sample DF. I. Z. Wahrsch. verw. Gebiete 32, 111–131.CrossRefGoogle Scholar
Krasnosel'skiĭ, M. A., and Rutitskii, Ia. B. (1961). Convex Functions and Orlicz Spaces. Transl. from Russian by L. F., Boron. Noordhoff, Groningen.Google Scholar
Landau, H. J., and Shepp, Lawrence A. (1971). On the supremum of a Gaussian process. Sankhyā Ser. A 32, 369–378.Google Scholar
Lang, Serge (1993). Real and Functional Analysis, 3rd ed. of Real Analysis, Springer, New York.CrossRefGoogle Scholar
Ledoux, Michel (1996). Isoperimetry and Gaussian analysis. In Ecole d'èté de probabilités de St.-Flour, 1994, Lecture Notes in Math. (Springer) 1648, 165–294.Google Scholar
Ledoux, M. (2001). The Concentration of Measure Phenomenon, Math. Surveys and Monographs 89, American Mathematical Society, Providence, RI.Google Scholar
Ledoux, M., and Talagrand, M. (1991). Probability in Banach Spaces. Springer, Berlin.CrossRefGoogle Scholar
Lehmann, Erich L. (1986, 1991). Testing Statistical Hypotheses, 2nd ed. repr. 1997, Springer, New York.Google Scholar
Leighton, Thomas, and Shor, P. (1989). Tight bounds for minimax grid matching, with applications to the average case analysis of algorithms. Combinatorica 9, 161–187.CrossRefGoogle Scholar
Lorentz, G. G. (1966). Metric entropy and approximation. Bull. Amer. Math. Soc. 72, 903–937.CrossRefGoogle Scholar
Luxemburg, W. A. J., and Zaanen, A. C. (1956). Conjugate spaces of Orlicz spaces. Akad. Wetensch. Amsterdam Proc. Ser. A 59 = Indag. Math. 18, 217–228.Google Scholar
Luxemburg, W. A. J., and Zaanen, A. C. (1983). Riesz Spaces, vol. 2, North-Holland, Amsterdam.Google Scholar
Marcus, Michael B. (1974). The ε-entropy of some compact subsets of lp. J. Approximation Th. 10, 304–312.Google Scholar
Marcus, M. B., and Shepp, L. A. (1972). Sample behavior of Gaussian processes. Proc. Sixth Berkeley Symp. Math. Statist. Prob. (1970) 2, 423–441. University of California Press, Berkeley and Los Angeles.Google Scholar
Marczewski, E., and Sikorski, R. (1948). Measures in non-separable metric spaces. Colloq. Math. 1, 133–139.CrossRefGoogle Scholar
Mason, David M. (1998). Notes on the the KMT Brownian bridge approximation to the uniform empirical process. Preprint.Google Scholar
Mason, D. M., and van Zwet, Willem (1987). A refinement of the KMT inequality for the uniform empirical process. Ann. Probab. 15, 871–884.CrossRefGoogle Scholar
Massart, Pascal (1990). The tight constant in the Dvoretzky–Kiefer–Wolfowitz inequality. Ann. Probab. 18, 1269–1283.CrossRefGoogle Scholar
Mourier, Edith (1951), Lois de grands nombres et théorie ergodique. C. R. Acad. Sci. Paris 232, 923–925.Google Scholar
Mourier, E. (1953). Éléments aléatoires dans unespace de Banach. Ann. Inst. H. Poincaré 13, 161–244.Google Scholar
Nachbin, Leopoldo J. (1965). The Haar Integral. Transl. from Portuguese by L., Bechtolsheim. Van Nostrand, Princeton, NJ.Google Scholar
Nanjundiah, T. S. (1959). Note on Stirling's formula. Amer. Math. Monthly 66, 701–703.CrossRefGoogle Scholar
Natanson, I. P. (1957). Theory of Functions of a Real Variable, vol. 2, 2nd ed. Transl. by L. F., Boron, Ungar, New York, 1961.Google Scholar
Neveu, Jacques (1977). Processus ponctuels. Ecole d'été de probabilités de St.-Flour VI, 1976, Lecture Notes in Math. (Springer) 598, 249–445.Google Scholar
*Neyman, Jerzy (1935). Su un teorema concernente le cosidette statistiche sufficienti. Giorn. Ist. Ital. Attuari 6, 320–334.Google Scholar
Okamoto, Masashi (1958). Some inequalities relating to the partial sum of binomial probabilities. Ann. Inst. Statist. Math. 10, 29–35.Google Scholar
Olkin, I., and Pukelsheim, F. (1982). The distance between two random vectors with given dispersion matrices. Linear Algebra Appl. 48, 257–263.CrossRefGoogle Scholar
Ossiander, Mina (1987). A central limit theorem under metric entropy with L2 bracketing. Ann. Probab. 15, 897–919.CrossRefGoogle Scholar
Pachl, Jan K. (1979). Two classes of measures. Colloq. Math. 42, 331–340.CrossRefGoogle Scholar
Panchenko, Dmitry (2004). 18.465 Topics in Statistics, OpenCourseWare, MIT.Google Scholar
Pettis, Billy Joe (1938). On integration in vector spaces. Trans. Amer. Math. Soc. 44, 277–304.CrossRefGoogle Scholar
Pisier, Gilles (1981). Remarques sur un resultat non publié de B. Maurey. Séminaire d'Analyse Fonctionelle 1980–1981V.1–V.12. Ecole Polytechnique, Centre de Mathematiques, Palaiseau.Google Scholar
Pisier, G. (1983). Some applications of the metric entropy bound in harmonic analysis. In Banach Spaces, Harmonic Analysis, and Probability Theory, Proc. Univ. Connecticut 1980–1981, eds. R. C., Blei and S. J., Sidney, Lecture Notes in Math. (Springer) 995, 123–154.CrossRefGoogle Scholar
Pollard, David B. (1982). A central limit theorem for empirical processes. J. Austral. Math. Soc. Ser. A 33, 235–248.CrossRefGoogle Scholar
Pollard, D. (1982). A central limit theorem for k-means clustering. Ann. Probab. 10, 919–926.CrossRefGoogle Scholar
Pollard, D. (1984). Convergence of Stochastic Processes. Springer, New York.CrossRefGoogle Scholar
Pollard, D. (1985). New ways to prove central limit theorems. Econometric Theory 1, 295–314.CrossRefGoogle Scholar
Pollard, D. (1990). Empirical Processes: Theory and Applications. NSF-CBMS Regional Conference Series in Probab. and Statist. 2. Inst. Math. Statist. and Amer. Statist. Assoc.Google Scholar
Posner, Edward C., Rodemich, Eugene R., and Rumsey, Howard Jr. (1967). Epsilon entropy of stochastic processes. Ann. Math. Statist. 38, 1000–1020.CrossRefGoogle Scholar
Posner, E. C., Rodemich, E. R., and Rumsey, H. (1969). Epsilon entropy of Gaussian processes. Ann. Math. Statist. 40, 1272–1296.CrossRefGoogle Scholar
Price, G. B. (1940). The theory of integration. Trans. Amer. Math. Soc. 47, 1–50.CrossRefGoogle Scholar
Pyke, Ronald (1968). The weak convergence of the empirical process with random sample size. Proc. Cambridge Philos. Soc. 64, 155–160.CrossRefGoogle Scholar
Rademacher, Hans (1919). Über partielle und totale Differenzierbarkeit I. Math. Ann. 79, 340–359.Google Scholar
Radon, Johann (1921). Mengen konvexer Körper, die einen gemeinsamen Punkt enthalten. Math. Ann. 83, 113–115.CrossRefGoogle Scholar
Rao, B. V. (1971). Borel structures for function spaces. Colloq. Math. 23, 33–38.Google Scholar
Rao, C. Radhakrishna (1973). Linear Statistical Inference and Its Applications. 2nd ed. Wiley, New York.CrossRefGoogle Scholar
Reshetnyak, Yu. G. (1968). Generalized derivatives and differentiability almost everywhere. Mat. Sb. 75, 323–334 (Russian) = Math. USSR-Sb. 4, 293–302 (English transl.).Google Scholar
Rhee, WanSoo, and Talagrand, M. (1988). Exact bounds for the stochastic upward matching problem. Trans. Amer. Math. Soc. 307, 109–125.CrossRefGoogle Scholar
Rudin, Walter (1974). Real and Complex Analysis, 2nd ed. McGraw-Hill, New York.Google Scholar
Ryll-Nardzewski, C. (1953). On quasi-compact measures. Fund. Math. 40, 125–130.CrossRefGoogle Scholar
Sainte-Beuve, Marie-France (1974). On the extension of von Neumann–Aumann's theorem. J. Funct. Anal. 17, 112–129.CrossRefGoogle Scholar
Sauer, Norbert (1972). On the density of families of sets. J. Combin. Theory Ser. A 13, 145–147.CrossRefGoogle Scholar
Sazonov, Vyacheslav V. (1962). On perfect measures (in Russian). Izv. Akad. Nauk SSSR Ser. Mat. 26, 391–414.Google Scholar
Schaefer, Helmut H. (1966). Topological Vector Spaces. Macmillan, New York. 3rd printing, corrected, Springer, New York, 1971.Google Scholar
Schaerf, Henry M. (1947). On the continuity of measurable functions in neighborhood spaces. Portugaliae Math. 6, 33–44, 66.Google Scholar
Schaerf, H. M. (1948). On the continuity of measurable functions in neighborhood spaces II. Portugaliae Math. 7, 91–92.Google Scholar
Schläfli, Ludwig (1901, posth.). Theorie der vielfachen Kontinuität, republ. 1991, Cornell University Library, Ithaca, NY; also in Gesammelte Math. Abhandlungen I, Birkhäuser, Basel, 1950.CrossRefGoogle Scholar
Schmidt, Wolfgang M. (1975). Irregularities of distribution IX. Acta Arith. 27, 385–396.CrossRefGoogle Scholar
Schwartz, Laurent (1966). Sur le théorème du graphe fermé. C. R. Acad. Sci. Paris Sér. A 263, A602–605.Google Scholar
Shao, Jun, and Tu, Dongsheng (1995). The Jackknife and Bootstrap. Springer, New York.CrossRefGoogle Scholar
Shelah, Saharon (1972). A combinatorial problem: stability and order for models and theories in infinitary languages. Pacific J. Math. 41, 247–261.CrossRefGoogle Scholar
Shor, Peter W. (1986). The average-case analysis of some on-line algorithms for bin packing. Combinatorica 6, 179–200.CrossRefGoogle Scholar
Shorack, Galen, and Wellner, Jon A. (1986). Empirical Processes with Applications to Statistics. Wiley, New York.Google Scholar
Shortt, Rae M. (1983). Universally measurable spaces: an invariance theorem and diverse characterizations. Fund. Math. 121, 169–176.Google Scholar
Shortt, R. M. (1984). Combinatorial methods in the study of marginal problems over separable spaces. J. Math. Anal. Appl. 97, 462–479.Google Scholar
Singh, Kesar (1981). On the asymptotic accuracy of Efron's bootstrap. Ann. Statist. 9, 1187–1195.CrossRefGoogle Scholar
Skitovič, V. P. (1954). Linear combinations of independent random variables and the normal distribution law. Izv. Akad. Nauk SSSR Ser. Mat. 18, 185–200 (in Russian).Google Scholar
Skorohod, Anatoli V. (1956). Limit theorems for stochastic processes. Theory Probab. Appl. 1, 261–290.Google Scholar
Skorohod, A. V. (1976). On a representation of random variables. Theory Probab. Appl. 21, 628–632 (English), 645–648 (Russian).Google Scholar
Slepian, David (1962). The one-sided barrier problem for Gaussian noise. Bell Syst. Tech. J. 41, 463–501.CrossRefGoogle Scholar
*Smirnov, N. V. (1944). Approximate laws of distributions of random variables from empirical data. Uspekhi Mat. Nauk 10, 179–206 (in Russian).Google Scholar
Smoktunowicz, Agata (1997). A remark on Vapnik–Chervonienkis classes. Colloq. Math. 74, 93–98.CrossRefGoogle Scholar
Steele, J. Michael (1975). Combinatorial entropy and uniform limit laws. Ph. D. dissertation, mathematics, Stanford University, Stanford, CA.Google Scholar
Steele, J. M. (1978a). Existence of submatrices with all possible columns. J. Combin. Theory Ser. A 24, 84–88.CrossRefGoogle Scholar
Steele, J. M. (1978b). Empirical discrepancies and subadditive processes. Ann. Probab. 6, 118–127.CrossRefGoogle Scholar
Stein, Elias M., and Weiss, Guido (1971). Introduction to Fourier Analysis on Euclidean Spaces. Princeton University Press, Princeton, NJ.Google Scholar
Steiner, Jakob (1826). Einige Gesetze über die Theilung der Ebene und des Raumes. J. Reine Angew. Math. 1, 349–364.Google Scholar
Stone, Arthur H. (1948). Paracompactness and product spaces. Bull. Amer. Math. Soc. 54, 631–632.CrossRefGoogle Scholar
Strobl, Franz (1994). Zur Theorie empirischer Prozesse. Dissertation, Mathematik, Universität München.Google Scholar
Strobl, F. (1995). On the reversed sub-martingale property of empirical discrepancies in arbitrary sample spaces. J. Theoret. Probab. 8, 825–831.CrossRefGoogle Scholar
Sudakov, Vladimir N. (1969). Gaussian measures, Cauchy measures and ε-entropy. Soviet Math. Dokl. 10, 310–313.Google Scholar
Sudakov, V. N. (1971). Gaussian random processes and measures of solid angles in Hilbert space. Soviet Math. Dokl. 12, 412–415.Google Scholar
Sudakov, V. N. (1973). A remark on the criterion of continuity of Gaussian sample function. In Proc. Second Japan-USSR Symp. Probab. Theory, Kyoto, 1972, ed. G. Maruyama, Yu. V. Prokhorov; Lecture Notes in Math. (Springer) 330, 444–454.Google Scholar
Sun, Tze-Gong (1976). Draft Ph. D. dissertation, Mathematics, University of Washington, Seattle.
Sun, Tze-Gong, and Pyke, R. (1982). Weak convergence of empirical processes. Technical Report, Dept. of Statistics, University of Washington, Seattle.Google Scholar
Talagrand, Michel (1987). Regularity of Gaussian processes. Acta Math. (Sweden) 159, 99–149.CrossRefGoogle Scholar
Talagrand, M. (1992). A simple proof of the majorizing measure theorem. Geom. Funct. Anal. 2, 118–125.CrossRefGoogle Scholar
Talagrand, M. (1994). Matching theorems and empirical discrepancy computations using majorizing measures. J. Amer. Math. Soc. 7, 455–537.CrossRefGoogle Scholar
Talagrand, M. (2005). The Generic Chaining. Springer, Berlin.Google Scholar
Topsøe, Flemming (1970). Topology and Measure. Lecture Notes in Math. (Springer) 133.CrossRef
Uspensky, James V. (1937). Introduction to Mathematical Probability. McGraw-Hill, New York.Google Scholar
van der Vaart, Aad [W.] (1996). New Donsker classes. Ann. Probab. 24, 2128–2140.Google Scholar
van der Vaart, A. W., and Wellner, J. A. (1996). Weak Convergence and Empirical Processes. Springer, New York.CrossRefGoogle Scholar
Vapnik, Vladimir N., and Červonenkis, Alekseĭ Ya. (1968). Uniform convergence of frequencies of occurrence of events to their probabilities. Dokl. Akad. Nauk SSSR 181, 781–783 (Russian) = Sov. Math. Doklady 9, 915–918 (English).Google Scholar
Vapnik, V. N., and Červonenkis, A. Ya. (1971). On the uniform convergence of relative frequencies of events to their probabilities. Theory Probab. Appl. 16, 264–280 = Teor. Veroiatnost. i Primenen. 16, 264–279.CrossRefGoogle Scholar
Vapnik, V. N., and (Červonenkis, A. Ya. (1974). TeoriyaRaspoznavaniya Obrazov: Statisticheskie problemy obucheniya [Theory of Pattern Recognition; Statistical problems of learning; in Russian]. Nauka, Moscow. German ed.: Theorie der Zeichenerkennung, by W. N. Wapnik and A. J. Tscherwonenkis, transl. by K. G. Stöckel and B. Schneider, ed. S. Unger and K. Fritzsch. Akademie-Verlag, Berlin, 1979 (Elektronisches Rechnen und Regeln, Sonderband).Google Scholar
Vapnik, V. N., and Červonenkis, A. Ya. (1981). Necessary and sufficient conditions for the uniform convergence of means to their expectations. Theory Probab. Appl. 26, 532–553.Google Scholar
Vorob'ev, N. N. (1962). Consistent families of measures and their extensions. Theory Probab. Appl. 7, 147–163 (English), 153–169 (Russian).Google Scholar
Vulikh, B. Z. (1961). Introduction to the Theory of Partially Ordered Spaces (transl. from Russian by L. F., Boron, 1967). Wolters-Noordhoff, Groningen.Google Scholar
*Wasserstein [Vaserštein], L. N. (1969). Markov processes of spaces describing large families of automata. Prob. Information Transmiss. 5, 47–52.Google Scholar
Watson, D. (1969). On partitions of n points. Proc. Edinburgh Math. Soc. 16, 263–264.CrossRefGoogle Scholar
Wenocur, Roberta S., and Dudley, R. M. (1981). Some special Vapnik–Čservonenkis classes. Discrete Math. 33, 313–318.CrossRefGoogle Scholar
Whittaker, E. T., and Watson, G. N. (1927). Modern Analysis, 4th ed., Cambridge University Press, Cambridge, repr. 1962.Google Scholar
Wichura, Michael J. (1970). On the construction of almost uniformly convergent random variables with given weakly convergent image laws. Ann. Math. Statist. 41, 284–291.CrossRefGoogle Scholar
Wolfowitz, Jacob (1954). Generalization of the theorem of Glivenko–Cantelli. Ann. Math. Statist. 25, 131–138.CrossRefGoogle Scholar
Wright, F. T. (1981). The empirical discrepancy over lower layers and a related law of large numbers. Ann. Probab. 9, 323–329.CrossRefGoogle Scholar
Young, William Henry (1912). On classes of summable functions and their Fourier series. Proc. Roy. Soc. London Ser. A 87, 225–229.CrossRefGoogle Scholar
Zakon, Elias (1965). On “essentially metrizable” spaces and on measurable functions with values in such spaces. Trans. Amer. Math. Soc. 119, 443–453.Google Scholar
Ziegler, Klaus (1994). On functional central limit theorems and uniform laws of large numbers for sums of independent processes. Dissertation, Mathematik, Universität München.Google Scholar
*Ziegler, K. (1997a). A maximal inequality and a functional central limit theorem for set-indexed empirical processes. Results Math. 31, 189–194.CrossRefGoogle Scholar
*Ziegler, K. (1997b). On Hoffmann-Jørgensen-type inequalities for outer expectations with applications. Results Math. 32, 179–192.CrossRefGoogle Scholar
Ziemer, William P. (1989). Weakly Differentiable Functions. Springer, New York.CrossRefGoogle Scholar

Save book to Kindle

To save this book to your Kindle, first ensure coreplatform@cambridge.org is added to your Approved Personal Document E-mail List under your Personal Document Settings on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part of your Kindle email address below. Find out more about saving to your Kindle.

Note you can select to save to either the @free.kindle.com or @kindle.com variations. ‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi. ‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.

Find out more about the Kindle Personal Document Service.

  • Bibliography
  • R. M. Dudley, Massachusetts Institute of Technology
  • Book: Uniform Central Limit Theorems
  • Online publication: 05 June 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781139014830.022
Available formats
×

Save book to Dropbox

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Dropbox.

  • Bibliography
  • R. M. Dudley, Massachusetts Institute of Technology
  • Book: Uniform Central Limit Theorems
  • Online publication: 05 June 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781139014830.022
Available formats
×

Save book to Google Drive

To save content items to your account, please confirm that you agree to abide by our usage policies. If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account. Find out more about saving content to Google Drive.

  • Bibliography
  • R. M. Dudley, Massachusetts Institute of Technology
  • Book: Uniform Central Limit Theorems
  • Online publication: 05 June 2014
  • Chapter DOI: https://doi.org/10.1017/CBO9781139014830.022
Available formats
×