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- W2949716922 abstract "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 some general assumptions. These assumptions are in particular fulfilled 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." @default.
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- W2949716922 date "1998-02-23" @default.
- W2949716922 modified "2023-09-27" @default.
- W2949716922 title "Rademacher's theorem on configuration spaces and applications" @default.
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