{"paper":{"title":"Naively Haar null sets in Polish groups","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.LO","authors_text":"M\\'arton Elekes, Zolt\\'an Vidny\\'anszky","submitted_at":"2015-08-10T12:57:53Z","abstract_excerpt":"Let $(G,\\cdot)$ be a Polish group. We say that a set $X \\subset G$ is Haar null if there exists a universally measurable set $U \\supset X$ and a Borel probability measure $\\mu$ such that for every $g, h \\in G$ we have $\\mu(gUh)=0$. We call a set $X$ naively Haar null if there exists a Borel probability measure $\\mu$ such that for every $g, h \\in G$ we have $\\mu(gXh)=0$.\n  Generalizing a result of Elekes and Stepr\\=ans, which answers the first part of Problem FC from Fremlin's list, we prove that in every abelian Polish group there exists a naively Haar null set that is not Haar null."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1508.02227","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"}