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On the theory of Banach space valued multifunctions. I: Integration and conditional expectation. (English) Zbl 0579.28009
This paper studies the Aumann integral of Banach space valued multifunctions. It provides conditions under which this integral is weakly compact. This is done by proving a new weak compactness result for the Lebesgue-Bochner space $$L^ 1_ X(\Omega)$$ which generalizes an earlier one of Diestel. Also it examines multifunctions which depend on a parameter and provides conditions under which certain types of sets continuously are preserved by set-valued integration. Finally it examines some properties of the set-valued conditional expectation for integrable multifunctions.

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