ON THE SET OF POSITIVITY OF THE DENSITY O F WIENER FUNCTIONALS

Let f be an R(d)-valued Wiener-functional, which is smooth and non-deg enerate in the sense of the Malliavin calculus. Let p be the density, with respect to the Lebesgue measure in R(d), Of its law. We are inter ested in the set U = {p > 0} We prove, in particular, that U is a conn ected set. A consequence is that the intrinsic distance associated wit h f on U is a true distance (in particular; it is finite).