{"paper":{"title":"Haar null sets without $G_\\delta$ hulls","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.DS"],"primary_cat":"math.LO","authors_text":"M\\'arton Elekes, Zolt\\'an Vidny\\'anszky","submitted_at":"2013-12-30T09:42:33Z","abstract_excerpt":"Let $G$ be an abelian Polish group, e.g. a separable Banach space. A subset $X \\subset G$ is called Haar null (in the sense of Christensen) if there exists a Borel set $B \\supset X$ and a Borel probability measure $\\mu$ on $G$ such that $\\mu(B+g)=0$ for every $g \\in G$. The term shy is also commonly used for Haar null, and co-Haar null sets are often called prevalent.\n  Answering an old question of Mycielski we show that if $G$ is not locally compact then there exists a Borel Haar null set that is not contained in any $G_\\delta$ Haar null set. We also show that $G_\\delta$ can be replaced by an"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1312.7667","kind":"arxiv","version":4},"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"}