Hausdorff measurable multifunctions
type: Item
instance of: scholarly article
title: Hausdorff measurable multifunctions
zbMATH Open document ID: 0921.54013
author: Giulio Pianigiani
author: F. S. de Blasi
published in: Journal of Mathematical Analysis and Applications
publication date: 1999-09-26T00:00:00Z
review text: Several notions of measurability for multifunctions are introduced and their relations are explained. The main results concern multifunctions \(F\) defined on the product of two separable complete metric spaces, \(T\) and \(X\). The space \(T\) is endowed with the \(\sigma\)-algebra of measurable sets of a Borel measure \(\mu\) and \(X\) with the \(\sigma\)-algebra of its Borel sets. In both main results indicated below, \(F\) is supposed to be Hausdorff measurable in \((t,x)\) and Hausdorff upper semi-continuous in \(x\). One of the main results gives Hukuhara type approximations \(F_n\) of \(F\) that have Carathéodory selections \(f_n:T\times X\to E\), where \(E\) is a separable Banach space and the values of \(F\) are convex closed bounded nonempty subsets of \(E\). Another result is a theorem of Scorza-Dragoni type and it concerns \(F\) with values forming a separable subset of the hyperspace of closed bounded nonempty subsets of a metric space \(Z\).
Mathematics Subject Classification ID: 54C60
Mathematics Subject Classification ID: 28B20
zbMATH DE Number: 1246332
zbMATH Keywords: multifunctions
zbMATH Keywords: Hausdorff measurability
zbMATH Keywords: Hausdorff semi-continuity
reviewed by: Petr Holický
MaRDI profile type: Publication
full work available at URL: jmaa.1998.6060
OpenAlex ID: W2006226007
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DOI: 10.1006/JMAA.1998.6060
description: scientific article; zbMATH DE number 1246332