Existence of measures invariant with respect to a semigroup of continuous open mappings of a locally compact topological space
type: Item
instance of: scholarly article
title: Existence of measures invariant with respect to a semigroup of continuous open mappings of a locally compact topological space
zbMATH Open document ID: 0844.43001
DOI: 10.1007/BF02303975
author: V. V. Mukhin
published in: Mathematical Notes
publication date: 1996-02-21T00:00:00Z
review text: Let \(S\) be a semigroup of continuous and open mappings of a locally compact space \(X\). The purpose of the paper is to establish conditions under which there exists a left \(S\)-invariant measure on \(X\). The first theorem only establishes the existence of such a measure whose support is an orbit in \(X\). Here an orbit is defined to be a set closed under the smallest equivalence relation containing all pairs \((x,s (x))\). There are then three corollaries which establish conditions under which there is such a measure with support the whole of \(X\).
reviewed by: John W.Baker
Mathematics Subject Classification ID: 43A05
Mathematics Subject Classification ID: 22A20
zbMATH DE Number: 846501
zbMATH Keywords: invariant measure
zbMATH Keywords: semigroup
zbMATH Keywords: mappings
zbMATH Keywords: locally compact space
MaRDI profile type: Publication
cites work: Q3318992
full work available at URL: https://doi.org/10.1007/bf02303975
OpenAlex ID: W2051337479
description: scientific article; zbMATH DE number 846501