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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 $i\\geq 1$."},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"0802.2353","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.DS","submitted_at":"2008-02-16T22:30:48Z","cross_cats_sorted":["math.OA"],"title_canon_sha256":"3d63c1f7488247ad379c584244f00925ea228073f9ba373b108dd610ef20f93a","abstract_canon_sha256":"cee2d9f535a2afbb5734340832cad26194c90047a8b5a390d821b49bb873cb2a"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:40.786549Z","signature_b64":"foaUs3EDBWN1O0DvfHiWqF+c+rvTM6pvqSCPISTwaxASMNxOwvYHQ6KnyDpTQtEyKyULK+LbFkqNImrhR6tKAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"602fd7631354d82da797ac9d6eb77dd64f372728c1bba0f684e9f6585fddfe3c","last_reissued_at":"2026-05-18T00:22:40.785968Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:40.785968Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"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"},"aliases":[{"alias_kind":"arxiv","alias_value":"0802.2353","created_at":"2026-05-18T00:22:40.786070+00:00"},{"alias_kind":"arxiv_version","alias_value":"0802.2353v1","created_at":"2026-05-18T00:22:40.786070+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.0802.2353","created_at":"2026-05-18T00:22:40.786070+00:00"},{"alias_kind":"pith_short_12","alias_value":"MAX5OYYTKTMC","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_16","alias_value":"MAX5OYYTKTMC3J4X","created_at":"2026-05-18T12:25:57.157939+00:00"},{"alias_kind":"pith_short_8","alias_value":"MAX5OYYT","created_at":"2026-05-18T12:25:57.157939+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":0,"internal_anchor_count":0,"sample":[]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/MAX5OYYTKTMC3J4XVSOW5N352Z","json":"https://pith.science/pith/MAX5OYYTKTMC3J4XVSOW5N352Z.json","graph_json":"https://pith.science/api/pith-number/MAX5OYYTKTMC3J4XVSOW5N352Z/graph.json","events_json":"https://pith.science/api/pith-number/MAX5OYYTKTMC3J4XVSOW5N352Z/events.json","paper":"https://pith.science/paper/MAX5OYYT"},"agent_actions":{"view_html":"https://pith.science/pith/MAX5OYYTKTMC3J4XVSOW5N352Z","download_json":"https://pith.science/pith/MAX5OYYTKTMC3J4XVSOW5N352Z.json","view_paper":"https://pith.science/paper/MAX5OYYT","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=0802.2353&json=true","fetch_graph":"https://pith.science/api/pith-number/MAX5OYYTKTMC3J4XVSOW5N352Z/graph.json","fetch_events":"https://pith.science/api/pith-number/MAX5OYYTKTMC3J4XVSOW5N352Z/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MAX5OYYTKTMC3J4XVSOW5N352Z/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MAX5OYYTKTMC3J4XVSOW5N352Z/action/storage_attestation","attest_author":"https://pith.science/pith/MAX5OYYTKTMC3J4XVSOW5N352Z/action/author_attestation","sign_citation":"https://pith.science/pith/MAX5OYYTKTMC3J4XVSOW5N352Z/action/citation_signature","submit_replication":"https://pith.science/pith/MAX5OYYTKTMC3J4XVSOW5N352Z/action/replication_record"}},"created_at":"2026-05-18T00:22:40.786070+00:00","updated_at":"2026-05-18T00:22:40.786070+00:00"}