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Affine Baire-one functions on Choquet simplexes

Published online by Cambridge University Press:  17 April 2009

Jiří Spurný
Jiří Spurný
Affiliation:
Faculty of Mathematics and Physics, Charles University, Sokolovská 83, 186 75 Praha 8, Czech Republic, e-mail: spurny@karlin.mff.cuni.cz
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Metrisable Choquet simplexes with the set of extreme points being an Fσ-set are characterised by means of the behaviour of the space of affine Baire-one functions.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 71 , Issue 2 , April 2005 , pp. 235 - 258
Copyright
Copyright © Australian Mathematical Society 2005

References

[1]Alfsen, E.M., Compact convex sets and boundary integrals (Springer-Verlag, Berlin, Heidelberg, New York, 1971).CrossRefGoogle Scholar
[2]Asimow, L. and Ellis, A.J., Convexity theory and its applications in functional analysis, London Mathematical Society Monographs 16 (Academic Press, London, New York, 1980).Google Scholar
[3]Bauer, H., ‘Šilowscher Rand und Dirichletsches Problem’, Ann. Inst. Fourier (Grenoble) 11 (1961), 89–136.CrossRefGoogle Scholar
[4]Bauer, H., ‘Simplicial function spaces and simplexes’, Exposition Math. 3 (1985), 165–168.Google Scholar
[5]Bliedtner, J. and Hansen, W., ‘Simplicial cones in potential theory’, Inventiones Math. 29 (1975), 83–110.CrossRefGoogle Scholar
[6]Boboc, N. and Cornea, A., ‘Convex cones of lower semicontinuous functions on compact spaces’, Rev. Roumaine Math. Pures Appl. 12 (1967), 471–525.Google Scholar
[7]Choquet, G., ‘Remarque à propos de la démonstration de l'unicité de P.A. Meyer’, Séminaire Brelot-Choquet-Deny (Théorie de Potentiel) 8 (1961/1962), 6 e année.Google Scholar
[8]Choquet, G., Lectures on analysis I – III (W. A. Benjamin, Inc., New York, Amsterdam, 1969).Google Scholar
[9]Engelking, R., General Topology (Heldermann Verlag, Berlin, 1989).Google Scholar
[10]Hewitt, E. and Stromberg, K., Real and abstract analysis (Springer-Verlag, Berlin, Heidelberg, New York, 1969).Google Scholar
[11]Jellett, F., ‘On affine extensions of continuous functions defined on the extreme points of a Choquet simplex’, Quart. J. Math. Oxford Ser. (2) 36 (1985), 71–73.CrossRefGoogle Scholar
[12]Kechris, A.S., Classical descriptive set theory (Springer-Verlag, New York, 1995).CrossRefGoogle Scholar
[13]Kuratowski, K., Topology, Vol. I (Academic Press, New York, 1966).Google Scholar
[14]Lazar, A., ‘Spaces of affine continuous functions on simplexes’, Trans. Amer. Math. Soc. 134 (1968), 503–525.CrossRefGoogle Scholar
[15]Lukeš, J., Malý, J., Netuka, I., Smrčka, M. and Spurný, J., ‘On approximation of affine Baire-one functions’, Israel Jour. Math. 134 (2003), 255–289.CrossRefGoogle Scholar
[16]Lukeš, J., Malý, J. and Zajíček, L., Fine topology methods in real analysis and potential theory, Lecture Notes in Math. 1189 (Springer-Verlag, Berlin, Heldelberg, New York, 1986).CrossRefGoogle Scholar
[17]Netuka, I., ‘The Dirichlet problem for harmonic functions’, Amer. Math. Monthly 87 (1980), 621–628.CrossRefGoogle Scholar
[18]Rogalski, M., ‘Opérateurs de Lion, projecteurs boréliens et simplexes analytiques’, J. Funct. Anal. 2 (1968), 458–488.CrossRefGoogle Scholar
[19]Rogers, C.E. and Jayne, J.E., K-analytic sets (Academic Press, London, New York, 1980).Google Scholar
[20]Raymond, J. Saint, ‘Fonctions convexes de première classe’, Math. Scand. 54 (1984), 121–129.CrossRefGoogle Scholar
[21]Spurný, J., ‘On the Dirichlet problem for the functions of the first Baire class’, Comment. Math. Univ. Carolin. 42 (2001), 721–728.Google Scholar
[22]Spurný, J., ‘Representation of abstract affine functions’, Real. Anal. Exchange 28 (2002/2003), 337–354.CrossRefGoogle Scholar
[23]Talagrand, M., ‘Choquet simplexes whose set of extreme points is K-analytic’, Ann. Inst. Fourier (Grenoble) 35 (1985), 195–206.CrossRefGoogle Scholar