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Rademacher's Theorem on Configuration Spaces and Applications

✍ Scribed by Michael Röckner; Alexander Schied

Publisher
Elsevier Science
Year
1999
Tongue
English
Weight
281 KB
Volume
169
Category
Article
ISSN
0022-1236

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✦ Synopsis

We consider an L 2 -Wasserstein type distance \ on the configuration space 1 X over a Riemannian manifold X, and we prove that -Lipschitz functions are contained in a Dirichlet space associated with a measure on 1 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 \ 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 \ is optimal in the sense that it is the intrinsic metric of our Dirichlet form.

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