{"paper":{"title":"A new approach to Sobolev spaces in metric measure spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Tomas Sj\\\"odin","submitted_at":"2015-04-29T09:03:34Z","abstract_excerpt":"Let $(X,d_X,\\mu)$ be a metric measure space where $X$ is locally compact and separable and $\\mu$ is a Borel regular measure such that $0 <\\mu(B(x,r)) <\\infty$ for every ball $B(x,r)$ with center $x \\in X$ and radius $r>0$. We define $\\mathcal{X}$ to be the set of all positive, finite non-zero regular Borel measures with compact support in $X$ which are dominated by $\\mu$, and $\\mathcal{M}=\\mathcal{X} \\cup \\{0\\}$. By introducing a kind of mass transport metric $d_{\\mathcal{M}}$ on this set we provide a new approach to first order Sobolev spaces on metric measure spaces, first by introducing suc"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1504.07778","kind":"arxiv","version":2},"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"}