GROUP ACTIONS WITH TOPOLOGICALLY STABLE MEASURES

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 is an element of 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.