Recurrence and the existence of invariant measures

Manuel Inselmann; Benjamin Miller

doi:10.1017/jsl.2020.8

Recurrence and the existence of invariant measures

Manuel Inselmann, Benjamin Miller

Department of Mathematics

Publications: Contribution to journal › Article › Peer Reviewed

Abstract

We show that recurrence conditions do not yield invariant Borel probability measures in the descriptive set-theoretic milieu, in the strong sense that if a Borel action of a locally compact Polish group on a standard Borel space satisfies such a condition but does not have an orbit supporting an invariant Borel probability measure, then there is an invariant Borel set on which the action satisfies the condition but does not have an invariant Borel probability measure.

Original language	English
Pages (from-to)	60-76
Number of pages	17
Journal	Journal of Symbolic Logic
Volume	86
Issue number	1
DOIs	https://doi.org/10.1017/jsl.2020.8
Publication status	Published - Mar 2021

Austrian Fields of Science 2012

101013 Mathematical logic
101027 Dynamical systems

Keywords

Invariant measure, recurrence, transience, wandering
recurrence
COCYCLE
transience
invariant measure
BOREL
wandering

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10.1017/jsl.2020.8

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Recurrence and the existence of invariant measures

Abstract

Austrian Fields of Science 2012

Keywords

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