{"paper":{"title":"Measure-theoretic chaos (Chaos au sens de la mesure)","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.PR"],"primary_cat":"math.DS","authors_text":"Tomasz Downarowicz, Yves Lacroix","submitted_at":"2011-11-10T08:47:09Z","abstract_excerpt":"We define new isomorphism-invariants for ergodic measure-preserving systems on standard probability spaces, called measure-theoretic chaos and measure-theoretic$^+$ chaos. These notions are analogs of the topological chaoses {\\rm DC2} and its slightly stronger version (which we denote by {\\rm DC}{\\small$1\\tfrac12$}). We prove that: 1. If a \\tl\\ system is measure-theoretically (measure-theoretically$^+$) chaotic with respect to at least one of its ergodic measures then it is \\tl ly {\\rm DC2} ({\\rm DC}{\\small$1 \\tfrac12$}) chaotic. 2. Every ergodic system with positive Kolmogorov--Sinai entropy "},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1111.2420","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"}