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Transactions of the American Mathematical Society

ISSN 1088-6850(online) ISSN 0002-9947(print)



On the convergence of closed-valued measurable multifunctions

Authors: Gabriella Salinetti and Roger J.-B. Wets
Journal: Trans. Amer. Math. Soc. 266 (1981), 275-289
MSC: Primary 28A20; Secondary 54C60
MathSciNet review: 613796
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Abstract: In this paper we study the convergence almost everywhere and in measure of sequences of closed-valued multifunctions. We first give a number of criteria for the convergence of sequences of closed subsets. These results are used to obtain various characterizations for the convergence of measurable multifunctions. In particular we are interested in the convergence properties of (measurable) selections.

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Keywords: Measurable multifunction, measurable selection, convergence in probability, convergence almost everywhere, hyperspaces, convergence in hyperspaces
Article copyright: © Copyright 1981 American Mathematical Society