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The Sobolev regularity of invariant measures for diffusion processes isproved on non-smooth metric measure spaces with synthetic lower Ricci curvaturebounds. As an application, the symmetrizability of semigroups is characterized,and the stability of invariant measures is proved under perturbations of driftsand the underlying spaces in the sense of the measured Gromov convergence.

Regularity and Stability of Invariant Measures for Diffusion Processes under Synthetic Lower Ricci Curvature Bounds