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On weak convergence implying strong convergence in L1-spaces

Published online by Cambridge University Press:  17 April 2009

Erik J. Balder
Erik J. Balder
Affiliation:
Mathematical Institute, University of Utrecht, PO Box 80.010, 3508 TA Utrecht, The Netherlands.
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Abstract

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Recently, Visintin gave conditions under which weak convergence in L1 (T;RN) implies strong convergence. Here we analyze such results in terms of associated young measures and present an extension to L1 (T;Ξ), where Ξ is a separable reflexive Banach space.

Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 33 , Issue 3 , June 1986 , pp. 363 - 368
Copyright
Copyright © Australian Mathematical Society 1986

References

[1]Alfsen, Erik M., Compact convex sets and boundary integrals (Springer-Verlag, Berlin, Heidelberg, New York, 1971).CrossRefGoogle Scholar
[2]Balder, E.J., “A general approach to lower semicontinuity and lower closure in optimal control theory”, SIAM J. Control Optim., 22 (1984), 570–598.CrossRefGoogle Scholar
[3]Balder, E.J., “An extension of Prohorov's theorem for transition probabilities with applications to infinite-dimensional lower closure problems”, Rend. Circ. Mat. Palermo, 34 (3) (1985). (in press)CrossRefGoogle Scholar
[4]Brooks, James K. and Dinculeanu, N., “Weak compactness in spaces of Bochner integrable functions and applications”, Adv. In Math., 24 (1977), 172–188.CrossRefGoogle Scholar
[5]Dinculeanu, N., Vector measures (Deutscher Verlag der Wissenschaften, Berlin, 1966).Google Scholar
[6]DiPerna, Ronald J., “Measure-valued solutions to conservation laws”, Arch. Rational Mech. Anal., 88 (1985), 223–270.CrossRefGoogle Scholar
[7]Neveu, Jacques, Bases mathématiques du calcul des probablilités (Masson, Paris, 1964; English Transl. Holden-Day, San Fransisco, London Amsterdam 1965).Google Scholar
[8]Visintin, A., “Strong convergence results related to strict convexity”, Comm. Partical Differential Equations, 9 (1984), 439–466.CrossRefGoogle Scholar