On the integrable selections of certain multifunctions
type: Item
instance of: scholarly article
title: On the integrable selections of certain multifunctions
zbMATH Open document ID: 0859.28007
DOI: 10.1007/BF00419375
author: Biagio Ricceri
published in: Set-Valued Analysis
publication date: 1997-04-06T00:00:00Z
review text: Let \(F:T\to E\) be a closed valued measurable multifunction from a nonatomic \(\sigma\)-finite measure space \(T\) into a separable Banach space \(E\). Conditions are formulated under which the set of all integrable selections of \(F\) intersects each member of a specially defined family \(\mathfrak V\) of subsets of \(L^1(T,E)\). Among examples of \(\mathfrak V\) there is a family of all closed hyperplanes of \(L^1\). There are indicated many consequences, e.g., concerning relations between convergence of sequences of multifunctions and its selectors, further, properties of Aumann integral, Gâteaux differentiability of the Nemytski operator, etc.
Mathematics Subject Classification ID: 28B20
Mathematics Subject Classification ID: 49J45
Mathematics Subject Classification ID: 49J50
zbMATH DE Number: 898041
zbMATH Keywords: measurable multifunction
zbMATH Keywords: integrable selections
zbMATH Keywords: Aumann integral
zbMATH Keywords: Gâteaux differentiability
zbMATH Keywords: Nemytski operator
reviewed by: Włodzimierz Ślęzak
MaRDI profile type: Publication
cites work: Some topological mini-max theorems via an alternative principle for multifunctions
cites work: Q4880613
cites work: Connectedness of sublevels of integral functionals
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description: scientific article; zbMATH DE number 898041