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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"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1711.08918","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.AP","submitted_at":"2017-11-24T10:28:37Z","cross_cats_sorted":[],"title_canon_sha256":"34914c69baf83cee9fc9467df094cb9915084640098a2413edda2b4ae8ae9165","abstract_canon_sha256":"57b408fedc291920636eba868ed13d9ac1526b518f035752b278e00430b805b9"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:29:41.737166Z","signature_b64":"la5SH5iXIexgLHjZeGzBvVsAZ7nzXJcBgDUOs+02zrc1p5HxoGHEt6DQpldIoa5pj+QiCk3SS2VIybVAXAjiDQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"3e8367a7bfb0f7470f89c325b33ced06ace30a7ef3dba60c71bbb4167bea4285","last_reissued_at":"2026-05-18T00:29:41.736515Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:29:41.736515Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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 $X$. 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