On local properties of k-parameter semiflows of nonsingular point transformations
type: Item
instance of: scholarly article
title: On local properties of k-parameter semiflows of nonsingular point transformations
zbMATH Open document ID: 0611.28008
DOI: 10.1007/BF01950277
published in: Acta Mathematica Hungarica
publication date: 1984-01-01T00:00:00Z
review text: Let \((\vartheta_ t:\) \(t\in (0,\infty)^ k)\) be a measurable semigroup of nonsingular transformations of a \(\sigma\)-finite measure space and \(\{T_ t\}\) the semigroup of contractions in \(L_ 1\) with \(<T_ tf,g>=<f,g\circ \vartheta_ t>\) for \(f\in L_ 1,\quad g\in L_{\infty}.\) It is shown that \(\{T_ t\}\) is strongly continuous. \(\{T_ t\}\) is strongly continuous on \([0,\infty)^ k\) with \(T_ 0=id\) iff \(\mu (E)>0\) implies \(\mu (\vartheta_ t^{-1}E)>0\) for some \(t>0.\)
reviewed by: Ulrich Krengel
Mathematics Subject Classification ID: 28D99
Mathematics Subject Classification ID: 47A35
zbMATH DE Number: 3987609
zbMATH Keywords: ergodic properties of k-parameter measurable semiflows
zbMATH Keywords: measurable semigroup of nonsingular transformations
author: Ryotaro Sato
MaRDI profile type: Publication
cites work: Differentiation of n-Dimensional Additive Processes
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description: scientific article; zbMATH DE number 3987609