Rademacher's Theorem for Wiener Functionals

Abstract

Given an $\mathbb{R}$-valued, Borel measurable function $F$ on an abstract Wiener space $(E, H, \mu)$, we show that $F$ is uniformly Lipschitz continuous in the directions of $H$ if and only if it has one derivative in the sense of Malliavin and that derivative is an element of $L^\infty(\mu; H)$.