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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

Type
Article accepté pour publication ou publié
Date
1998
Journal name
Set-Valued Analysis
Volume
6
Number
3
Publisher
Springer
Pages
209-236
Publication identifier
http://dx.doi.org/10.1023/A:1008690517467
Metadata
Show full item record
Author(s)
Hess, Christian
Barbati, Alberto
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 / Keywords
set-valued map; hyperspace; Effros measurability; scalar measurability; analytic space; convex sets

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