{"paper":{"title":"Hausdorff dimension and $\\sigma$ finiteness of $p-$harmonic measures in space when $p\\geq n$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrew Vogel, John Lewis, Murat Akman","submitted_at":"2013-06-24T13:24:28Z","abstract_excerpt":"In this paper we study a p harmonic measure, associated with a positive p harmonic function \\hat{u} defined in an open set O, subset of R^n, and vanishing on a portion \\Gamma of boundary of O. If p>n we show that this p harmonic measure is concentrated on a set of \\sigma- finite H^{n-1} measure while if p=n the same conclusion holds provided \\Gamma is uniformly fat in the sense of n capacity."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5617","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"}