PUB - Publikationen an der Universität Bielefeld

We consider an L-2-Wasserstein type distance rho on the configuration space Gamma(X) over a Riemannian manifold, X, and we prove that rho-Lipschitz functions are contained in a Dirichlet space associated with a measure on Gamma(X) satisfying certain natural assumptions. These assumptions are in particular fulfilled by the classical Poisson measures and by a large class of tempered grandcanonical Gibbs measures with respect to a superstable lower regular pair potential. As an application we prove a criterion in terms of rho for a set to be exceptional. This result immediately implies, for instance, a quasi-sure version of the spatial ergodic theorem. We also show that rho is optimal in the sense that it is the intrinsic metric of our Dirichlet form. (C) 1999 Academic Press.