On the convexity and compactness of the integral of a Banach space valued correspondence

Konrad Podczeck

Journal of Mathematical Economics, 2008, vol. 44, issue 7-8, 836-852

Abstract: We characterize the class of finite measure spaces which guarantee that for a correspondence [phi] from to a general Banach space the Bochner integral of [phi] is convex. In addition, it is shown that if [phi] has weakly compact values and is integrably bounded, then, for this class of measure spaces, the Bochner integral of [phi] is weakly compact, too. Analogous results are provided with regard to the Gelfand integral of correspondences taking values in the dual of a separable Banach space, with "weakly compact" replaced by "weak*-compact." The crucial condition on the measure space concerns its measure algebra and is consistent with having T=[0,1] and [mu] to be an extension of Lebesgue measure.

Date: 2008
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Citations: View citations in EconPapers (26)

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Persistent link: https://EconPapers.repec.org/RePEc:eee:mateco:v:44:y:2008:i:7-8:p:836-852

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