Summary: In white noise theory on Hilbert spaces, it is known that maps which are uniformly continuous around the origin in the \(S\)-topology constitute an important class of “physical” random variables. We prove that random variables having such a continuity property can be approximated in the Gaussian measure by polynomial random variables. The proof relies on representing functions which are uniformly \(S\)-continuous around the origin as the composition of a continuous map with a Hilbert-Schmidt operator.