Relatively Compact Sets on Abstract Wiener Space

In this note, we obtain a sufficient and necessary condition for a set in an abstract Wiener space (X, H, µ) to be relatively compact in L 2(X, µ). Meanwhile, we give a sufficient condition for relative compactness in L p(X, µ) for p > 1. We also provide an example of Da Prato.Malliavin.Nualart to show the result.