Recurrence and the existence of invariant measures
Logic
2023-06-22 v1 Dynamical Systems
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.
Keywords
Cite
@article{arxiv.2002.09308,
title = {Recurrence and the existence of invariant measures},
author = {Manuel J. Inselmann and Benjamin D. Miller},
journal= {arXiv preprint arXiv:2002.09308},
year = {2023}
}
Comments
To appear in the Journal of Symbolic Logic