Measure topologically stable flows

Topological stability is a kind of stability for given dynamical systems in which continuous perturbations are allowed. Very recently, the concept of topological stability for Borel measures with respect to a given homeomorphism was introduced by Lee and Morales in [7]. In this paper, we introduce a notion of measure topological stability for a continuous flow, and prove that if every measure expansive flow has measure shadowing property then it is measure topologically stable.