{"paper":{"title":"On indecomposable sets with applications","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.AP","authors_text":"Andrew Lorent","submitted_at":"2013-05-14T19:52:30Z","abstract_excerpt":"In this note we show the characteristic function of every indecomposable set $F$ in the plane is $BV$ equivalent to the characteristic function a closed set $\\mathbb{F}$, i.e. $||\\mathbb{1}_{F}-\\mathbb{1}_{\\mathbb{F}}||_{BV(\\mathbb{R}^2)}=0$. We show by example this is false in dimension three and above. As a corollary to this result we show that for every $\\epsilon>0$ a set of finite perimeter $S$ can be approximated by a closed subset $\\mathbb{S}_{\\epsilon}$ with finitely many indecomposable components and with the property that $H^1(\\partial^M \\mathbb{S}_{\\epsilon}\\backslash \\partial^M S)=0"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1305.3264","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"}