Invariant measures of set-valued maps
type: Item
instance of: scholarly article
title: Invariant measures of set-valued maps
zbMATH Open document ID: 0989.47039
published in: Journal of Mathematical Analysis and Applications
publication date: 2002-08-01T00:00:00Z
review text: The author remarks that standard definition of an invariant measure requires that the function be univalued. However, recent applications [cf. \textit{Z. Artstein}, J. Differential Equations 152, No. 2, 289-307 (1999; Zbl 0923.34013)] have raised the need for an analogous notion of invariant measures for multifunctions. The author in this very interesting paper displayed five natural suggestions for the notion and examined when they are equivalent. It is proved that four of his definitions are equivalent when the underlying space is is a separable and complete metric space, and the fifth one is equivalent to them if, in addition, the space is locally compact and the set-valued map has a closed graph.
reviewed by: Themistocles M. Rassias
Mathematics Subject Classification ID: 47H04
Mathematics Subject Classification ID: 28C10
Mathematics Subject Classification ID: 34A60
zbMATH DE Number: 1563087
zbMATH Keywords: Markov transition function
zbMATH Keywords: Markov invariant
zbMATH Keywords: probability measure
zbMATH Keywords: invariant measures for multifunctions
zbMATH Keywords: set-valued map
zbMATH Keywords: closed graph
MaRDI profile type: Publication
full work available at URL: jmaa.2000.7095
OpenAlex ID: W2079502677
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DOI: 10.1006/JMAA.2000.7095
author: Zvi Artstein
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description: scientific article; zbMATH DE number 1563087