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Convergence theorems for Banach space valued integrable multifunctions. (English) Zbl 0619.28009
In this work we generalize a result of Kato on the pointwise behavior of a weakly convergent sequence in the Lebesgue-Bochner spaces $$L^ P_ X(\Omega)(1\leq p\leq \infty).$$ Then we use that result to prove Fatou 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.

##### MSC:
 28B20 Set-valued set functions and measures; integration of set-valued functions; measurable selections 28B05 Vector-valued set functions, measures and integrals 46G10 Vector-valued measures and integration
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