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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

Weak convergence and weak compactness for multifunctions with values in a separable Banach space


Author: Nikolaos S. Papageorgiou
Journal: Proc. Amer. Math. Soc. 109 (1990), 677-687
MSC: Primary 28A20; Secondary 28B20, 46G10
MathSciNet review: 1013978
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Abstract: In this paper we extend the notion of weak convergence to Banach space valued integrable multifunctions. We prove some properties of this mode of convergence and we show that under certain hypotheses the space of uniformly bounded, $ w$-compact, convex valued integrable multifunctions is sequentially weakly complete. Then we prove two Dunford-Pettis type weak compactness theorems and we also show that the set valued conditional expectation is weakly continuous. Finally we present an application from control theory.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1990-1013978-6
PII: S 0002-9939(1990)1013978-6
Keywords: Integrably bounded multifunction, multimeasure, Dunford-Pettis theorem, multivalued Radon-Nikodym theorem, Mackey topology, set valued conditional expectation, mild solution, control system
Article copyright: © Copyright 1990 American Mathematical Society