{"paper":{"title":"Harmonic measure is rectifiable if it is absolutely continuous with respect to the co-dimension one Hausdorff measure","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.AP"],"primary_cat":"math.CA","authors_text":"Alexander Volberg, Jonas Azzam, Jos\\'e Mar\\'ia Martell, Mihalis Mourgoglou, Steve Hofmann, Svitlana Mayboroda, Xavier Tolsa","submitted_at":"2015-09-22T11:58:41Z","abstract_excerpt":"In the present paper we sketch the proof of the fact that for any open connected set $\\Omega\\subset\\mathbb{R}^{n+1}$, $n\\geq 1$, and any $E\\subset \\partial \\Omega$ with $0<\\mathcal{H}^n(E)<\\infty$, absolute continuity of the harmonic measure $\\omega$ with respect to the Hausdorff measure on $E$ implies that $\\omega|_E$ is rectifiable."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1509.06558","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"}