{
  "id": "math/9802131",
  "version": "v1",
  "published": "1998-02-23T00:00:00.000Z",
  "updated": "1998-02-23T00:00:00.000Z",
  "title": "Rademacher's theorem on configuration spaces and applications",
  "authors": [
    "Michael Röckner",
    "Alexander Schied"
  ],
  "journal": "Journal of Functional Analysis 169, No.2, 325-356 (1999)",
  "categories": [
    "math.PR"
  ],
  "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.",
  "revisions": [
    {
      "version": "v1",
      "updated": "1998-02-23T00:00:00.000Z"
    }
  ],
  "analyses": {
    "keywords": [
      "configuration space",
      "rademachers theorem",
      "application",
      "superstable lower regular pair potential",
      "wasserstein type distance"
    ],
    "tags": [
      "journal article"
    ],
    "note": {
      "typesetting": "TeX",
      "pages": 0,
      "language": "en",
      "license": "arXiv",
      "status": "editable",
      "adsabs": "1998math......2131R"
    }
  }
}