{"paper":{"title":"Generalized Orlicz spaces and Wasserstein distances for convex-concave scale functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.FA","authors_text":"Karl-Theodor Sturm","submitted_at":"2011-04-21T10:19:24Z","abstract_excerpt":"Given a strictly increasing, continuous function $\\vartheta:\\R_+\\to\\R_+$, based on the cost functional $\\int_{X\\times X}\\vartheta(d(x,y))\\,d q(x,y)$, we define the $L^\\vartheta$-Wasserstein distance $W_\\vartheta(\\mu,\\nu)$ between probability measures $\\mu,\\nu$ on some metric space $(X,d)$. The function $\\vartheta$ will be assumed to admit a representation $\\vartheta=\\phi\\circ\\psi$ as a composition of a convex and a concave function $\\phi$ and $\\psi$, resp. Besides convex functions and concave functions this includes all $\\mathcal C^2$ functions.\n  For such functions $\\vartheta$ we extend the c"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1104.4223","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"}