On the theory of Banach space valued multifunctions. I: Integration and conditional expectation (Q1067034)
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scientific article; zbMATH DE number 3927276
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | On the theory of Banach space valued multifunctions. I: Integration and conditional expectation |
scientific article; zbMATH DE number 3927276 |
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On the theory of Banach space valued multifunctions. I: Integration and conditional expectation (English)
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1985
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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.
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Hausdorff metric
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Radon-Nikodým property
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measurable selection
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James' theorem
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Aumann integral of Banach space valued multifunctions
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set- valued conditional expectation
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