{"paper":{"title":"Unavoidable sets and harmonic measures living on small sets","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Ivan Netuka, Wolfhard Hansen","submitted_at":"2013-06-23T16:23:45Z","abstract_excerpt":"Given a connected open set $U\\ne\\emptyset$ in $ R^d$, $d\\ge 2$, a relatively closed set $A$ in $U$ is called \\emph{unavoidable in $U$}, if Brownian motion, starting in $x\\in U\\setminus A$ and killed when leaving $U$, hits $A$ almost surely or, equivalently, if the harmonic measure for $x$ with respect to $U\\setminus A$ has mass $1$ on $A$. First a new criterion for unavoidable sets is proven which facilitates the construction of smaller and smaller unavoidable sets in $U$. Starting with an arbitrary champagne subdomain of $U$ (which is obtained omitting a locally finite union of pairwise disjo"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1306.5433","kind":"arxiv","version":2},"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"}