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International Journal of Mathematics and Mathematical Sciences
Volume 10, Issue 3, Pages 433-442
http://dx.doi.org/10.1155/S0161171287000516

Convergence theorems for Banach space valued integrable multifunctions

Department of Mathematics, University of California, Davis, California 95616, USA

Received 21 May 1986

Copyright © 1987 Hindawi Publishing Corporation. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Abstract

In this work we generalize a result of Kato on the pointwise behavior of a weakly convergent sequence in the Lebesgue-Bochner spaces LXP(Ω) (1p). Then we use that result to prove Fatou's type lemmata and dominated convergence theorems for the Aumann integral of Banach space valued measurable multifunctions. Analogous convergence results are also proved for the sets of integrable selectors of those multifunctions. In the process of proving those convergence theorems we make some useful observations concerning the Kuratowski-Mosco convergence of sets.