{"paper":{"title":"Every locally finite Borel measure on $\\mathbb{R}$ has conformal dimension zero","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Tuomas Orponen","submitted_at":"2017-05-14T13:17:12Z","abstract_excerpt":"A result of P. Tukia from 1989 says that Lebesgue measure on $\\mathbb{R}$ has conformal dimension zero: for every $\\epsilon > 0$, there is a Borel set $G \\subset \\mathbb{R}$ of full Lebesgue measure, and a quasisymmetric homeomorphism $f \\colon \\mathbb{R} \\to \\mathbb{R}$ such that $\\dim_{\\mathrm{H}} f(G) < \\epsilon$. In this short note, I show that the same is true for every locally finite Borel measure on $\\mathbb{R}$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1705.04961","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"}