Measurable selectors and set-valued Pettis integral in non-separable Banach spaces (Q1000529)
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scientific article; zbMATH DE number 5503521
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Measurable selectors and set-valued Pettis integral in non-separable Banach spaces |
scientific article; zbMATH DE number 5503521 |
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Measurable selectors and set-valued Pettis integral in non-separable Banach spaces (English)
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9 February 2009
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\textit{K. Kuratowski} and \textit{C. Ryll-Nardzewski}'s type selection theorem [Bull. Acad. Polon. Sci. Ser. Sci. Math. Astronom. Phys. 13, 397--403 (1965; Zbl 0152.21403)] and results about norm-Borel measurable selectors for multi-function satisfying stronger measurability properties are obtained for the range spaces without the requirements of separability. The Pettis integral \( \int_A F d \mu \) coincides with the closure of the set of integrals over \(A\) of all Pettis integrable selectors of \(F\).
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Pettis integral
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measurable selector
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Pettis integrable multi-function
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convex weakly compact set
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complete finite measure space
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