On the convergence of closed-valued measurable multifunctions

Salinetti, Gabriella; Wets, Roger J.-B.

doi:10.1090/S0002-9947-1981-0613796-3

On the convergence of closed-valued measurable multifunctions
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by Gabriella Salinetti and Roger J.-B. Wets PDF

Trans. Amer. Math. Soc. 266 (1981), 275-289 Request permission

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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