SRB measures for partially hyperbolic diffeomorphisms with the mostly contracting center

In this paper, we study the SRB (Sinai-Ruelle-Bowen) measures for partially hyperbolic diffeomorphisms with the mostly contracting center. For such kinds of diffeomorphisms, we prove the existence, finiteness, and basin covering property of these SRB measures. Furthermore, we prove that Lebesgue almost every point in the basin is Lyapunov regular.