A note on Lusin-type approximation of Sobolev functions on Gaussian spaces

We establish new approximation results in the sense of Lusin for Sobolev functions $f$ with $\mathrm{\mid }\mathrm{\nabla }f\mathrm{\mid }\in L\log L$ on infinite-dimensional spaces equipped with Gaussian measures. The proof relies on some new pointwise estimate for the approximations based on the corresponding semigroup which can be of independent interest.