{"paper":{"title":"Rademacher's theorem on configuration spaces and applications","license":"","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Alexander Schied, Michael R\\\"ockner","submitted_at":"1998-02-23T00:00:00Z","abstract_excerpt":"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"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9802131","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}