# GROUP ACTIONS WITH TOPOLOGICALLY STABLE MEASURES

 Title GROUP ACTIONS WITH TOPOLOGICALLY STABLE MEASURES Publication Type Journal Article Year of Publication 2018 Authors DONG MEIHUA, KIM SANGJIN, YIN JIANDONG Journal Dynamic Systems and Applications Volume 27 Issue 1 Start Page 185 Pagination 16 Date Published 01/2018 ISSN 1056-2176 AMS Subject Classification 37C85, 54H20 Abstract We prove that if an action $T$ of a finitely generated group $G$ on a compact metric space $X$ is measure expansive and has the measure shadowing property then it is measure topologically stable. This represents a measurable version of the main result in [4]. Moreover we prove that if $G$ is a finitely generated virtually nilpotent group and there exists $g \in G$ such that $T_g$ is expansive and has the invariant measure shadowing property then $T$ is invariant measure topologically stable. Finally we show that minimal actions approximated by periodic ones have no topologically stable measures. PDF https://www.acadsol.eu/dsa/articles/27/1/10.pdf DOI 10.12732/dsa.v27i1.10 Refereed Designation Refereed