{"paper":{"title":"Nearly hyperharmonic functions are infima of excessive functions","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Ivan Netuka, Wolfhard Hansen","submitted_at":"2018-09-23T15:04:04Z","abstract_excerpt":"Let $\\mathfrak X$ be a Hunt process on a locally compact space $X$ such that the set $\\mathcal E_{\\mathfrak X}$ of its Borel measurable excessive functions separates points, every function in $\\mathcal E_{\\mathfrak X}$ is the supremum of its continuous minorants in $\\mathcal E_{\\mathfrak X}$ and there are strictly positive continuous functions $v,w\\in\\mathcal E_{\\mathfrak X}$ such that $v/w$ vanishes at infinity.\n  A numerical function $u\\ge 0$ on $X$ is said to be nearly hyperharmonic, if $\\int^\\ast u\\circ X_{\\tau_V}\\,dP^x\\le u(x)$ for all $x\\in X$ and relatively compact open neighborhoods $V"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1809.08611","kind":"arxiv","version":3},"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"}