Title: Lusin-type approximation of Sobolev by Lipschitz functions, in Gaussian and $RCD(K,\infty)$ spaces,
Abstract: We establish new approximation results, in the sense of Lusin, of Sobolev
functions by Lipschitz ones, in some classes of non-doubling metric measure
structures. Our proof technique relies upon estimates for heat semigroups and
applies to Gaussian and $RCD(K, \infty)$ spaces. As a consequence, we obtain
quantitative stability for regular Lagrangian flows in Gaussian settings.