Continuous selections of Aumann integrals
type: Item
instance of: scholarly article
title: Continuous selections of Aumann integrals
zbMATH Open document ID: 0704.28006
DOI: 10.1016/0022-247X(90)90411-8
author: Andrzej Fryszkowski
published in: Journal of Mathematical Analysis and Applications
publication date: 1990-01-01T00:00:00Z
review text: Let K be a lower semicontinuous multifunction defined on a locally compact Polish space, whose values are closed decomposable subsets of the Lebesgue space \(L^ 1.\) It is proved, that for every continuous selection of the Aumann integral of K and for every \(\epsilon >0\) there exists a continuous selection k of K such that the uniform distance between the integral of k and the given selection of the Aumann integral of K is smaller than \(\epsilon\). Some interpretations of the above result for a family of vector measures and a theorem concerning Carathéodory's selections are also included.
Mathematics Subject Classification ID: 28B20
Mathematics Subject Classification ID: 54C65
Mathematics Subject Classification ID: 26E25
zbMATH DE Number: 4154790
zbMATH Keywords: lower semicontinuous multifunction
zbMATH Keywords: continuous selection
zbMATH Keywords: Aumann integral
zbMATH Keywords: vector measures
zbMATH Keywords: Carathéodory's selections
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 4154790