{"paper":{"title":"Bruckner--Garg-type results with respect to Haar null sets in $C[0,1]$","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"M\\'arton Elekes, Rich\\'ard Balka, Udayan B. Darji","submitted_at":"2013-11-21T02:27:44Z","abstract_excerpt":"A set $\\mathcal{A}\\subset C[0,1]$ is \\emph{shy} or \\emph{Haar null } (in the sense of Christensen) if there exists a Borel set $\\mathcal{B}\\subset C[0,1]$ and a Borel probability measure $\\mu$ on $C[0,1]$ such that $\\mathcal{A}\\subset \\mathcal{B}$ and $\\mu\\left(\\mathcal{B}+f\\right) = 0$ for all $f \\in C[0,1]$. The complement of a shy set is called a \\emph{prevalent} set. We say that a set is \\emph{Haar ambivalent} if it is neither shy nor prevalent.\n  The main goal of the paper is to answer the following question: What can we say about the topological properties of the level sets of the preval"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1311.5293","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"}