{"paper":{"title":"Semipolar sets and intrinsic Hausdorff measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ivan Netuka, Wolfhard Hansen","submitted_at":"2017-11-24T10:28:37Z","abstract_excerpt":"Given a \"Green function\" $G$ on a locally compact space $X$ with countable base, a Borel set $A$ in $X$ is called $G$-semipolar, if there is no measure $\\nu\\ne 0$ supported by $A$ such that $G\\nu:=\\int G(\\cdot,y)\\,d\\nu(y)$ is a continuous real function on $X$. Introducing an intrinsic Hausdorff measure $m_G$ using $G$-balls $B(x,\\rho):=\\{y\\in X\\colon G(x,y)>1/\\rho\\}$, it is shown that every set $A$ in $X$ with $m_G(A)<\\infty$ is contained in a $G$-semipolar Borel set.\n  This is of interest, since $G$-semipolar sets are semipolar in the potential-theoretic sense (countable unions of totally thi"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.08918","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"}