SOME REMARKS ON RADEMACHERS THEOREM IN INFINITE DIMENSIONS

We provide an infinite dimensional version of Rademacher's theorem in a linear space provided with a bounded Radon measure mu. The underlyin g concepts of the Lipschitz property and differentiability hold mu-alm ost everywhere and only in the linear subspace of directions along whi ch mu is quasiinvariant. The particular case where (X, mu) is the Wien er space (and for which the subspace of quasiinvariance coincides with the Cameron-Martin space) was proved in Enchev and Stroock (1993).