On the convexity and compactness of the integral of a Banach space valued correspondence
AbstractWe 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.
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Bibliographic InfoArticle provided by Elsevier in its journal Journal of Mathematical Economics.
Volume (Year): 44 (2008)
Issue (Month): 7-8 (July)
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- Barlo, Mehmet & Carmona, Guilherme, 2011. "Strategic behavior in non-atomic games," MPRA Paper 35549, University Library of Munich, Germany.
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Springer, vol. 50(3), pages 527-545, August.
- Wang, Jianwei & Zhang, Yongchao, 2010. "Purification, Saturation and the Exact Law of Large Numbers," MPRA Paper 22119, University Library of Munich, Germany.
- Sun, Yeneng & Zhang, Yongchao, 2008.
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- Michael Greinecker & Konrad Podczeck, 2013. "Liapounoff's vector measure theorem in Banach spaces," Working Papers 2013-20, Faculty of Economics and Statistics, University of Innsbruck.
- Carmona, Guilherme & Podczeck, Konrad, 2009.
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