Topological stability and pseudo-orbit tracing property of Borel measures from the viewpoint of open covers

Abstract

In the paper, we introduce the concepts of topological stability, expansivity and pseudo-orbit tracing property of Borel measures with respect to a given continuous map on a compact topological space from the viewpoint of open covers and prove that every expansive Borel measure with the pseudo-orbit tracing property is topologically stable. Furthermore, we obtain some properties of topologically stable measures.