{"paper":{"title":"Ergodic Subequivalence Relations Induced by a Bernoulli Action","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.DS","authors_text":"Adrian Ioana, Ionut Chifan","submitted_at":"2008-02-16T22:30:48Z","abstract_excerpt":"Let $\\Gamma$ be a countable group and denote by $\\Cal S$ the equivalence relation induced by the Bernoulli action $\\Gamma\\curvearrowright [0,1]^{\\Gamma}$, where $[0,1]^{\\Gamma}$ is endowed with the product Lebesgue measure. We prove that for any subequivalence relation $\\Cal R$ of $\\Cal S$, there exists a partition $\\{X_i\\}_{i\\geq 0}$ of $[0,1]^{\\Gamma}$ with $\\Cal R$-invariant measurable sets such that $\\Cal R_{|X_0}$ is hyperfinite and $\\Cal R_{|X_i}$ is strongly ergodic (hence ergodic), for every $i\\geq 1$."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"0802.2353","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"}