{"paper":{"title":"Stability of products of equivalence relations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.OA"],"primary_cat":"math.DS","authors_text":"Amine Marrakchi","submitted_at":"2017-09-01T15:04:26Z","abstract_excerpt":"An ergodic p.m.p. equivalence relation $ \\mathcal{R}$ is said to be stable if $\\mathcal{R} \\cong \\mathcal{R} \\times \\mathcal{R}_0$ where $\\mathcal{R}_0$ is the unique hyperfinite ergodic type $\\mathrm{II}_1$ equivalence relation. We prove that a direct product $\\mathcal{R} \\times \\mathcal{S}$ of two ergodic p.m.p. equivalence relations is stable if and only if one of the two components $\\mathcal{R}$ or $\\mathcal{S}$ is stable. This result is deduced from a new local characterization of stable equivalence relations. The similar question on McDuff $\\mathrm{II}_1$ factors is also discussed and so"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1709.00357","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"}