The Largest Class of Closed Convex Valued Multifunctions for which Effros Measurability and Scalar Measurability Coincide
Hess, Christian; Barbati, Alberto (1998), The Largest Class of Closed Convex Valued Multifunctions for which Effros Measurability and Scalar Measurability Coincide, Set-Valued Analysis, 6, 3, p. 209-236. http://dx.doi.org/10.1023/A:1008690517467
TypeArticle accepté pour publication ou publié
Journal nameSet-Valued Analysis
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Abstract (EN)This paper deals with the comparison of Effros measurability and scalar measurability for multifunctions whose values lie in C(X), the set of closed convex subsets of a normed linear space X. An introductory counter-example shows that, on C(X), the Effros measurability is strictly stronger than the scalar measurability. Then, we introduce the notion of countably supported subspace of C(X). After some preparatory results and examples about this class of convex subsets, we show that on an analytic countably supported subspace of C(X), the Effros and the scalar C of C(X), nonnecessarily analytic, the Effros and scalar C is countably supported. This leads us to exhibit and study a wide class of subspaces of C(X) both countably supported and analytic. At last, we compare our results with the already existing ones and we briefly show how our main results can be extended to the case where X is a locally convex vector space.
Subjects / Keywordsset-valued map; hyperspace; Effros measurability; scalar measurability; analytic space; convex sets
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