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Contributions to the theory of set valued functions and set valued measures. (English) Zbl 0634.28004
The author studies measurable multifunctions and multimeasures with values in a Banach space X. He proves a variation of the known Dunford theorem on weak compactness of subsets of the space \(L^ 1(X)\) and a Dunford-Pettis type theorem for sequences of integrably bounded multifunctions. Next he gives a representation theorem for additive set valued operators defined on \(L^ 1(X)\) and some pointwise weak compactness results for multifunctions with weakly compact set of Bochner integrable selectors. Finally he determines various properties of transition multimeasures.
Reviewer: K.Nikodem

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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