Topological stability and pseudo-orbit tracing property for expansive measures

We extend the concepts of topological stability and pseudo-orbit tracing properties from homeomorphisms to Borel measures. We prove that every expansive measure with the pseudo-orbit tracing property is topologically stable. This represents a measurable version of the classical result by Walters [28]. Afterwards, we derive some properties of the topologically stable measures and measures with the pseudo-orbit tracing property on compact metric spaces.