{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2018:MZLFQ52KKWIGLQVNPROBVRTYY5","short_pith_number":"pith:MZLFQ52K","schema_version":"1.0","canonical_sha256":"665658774a559065c2ad7c5c1ac678c77aadc4117150e9a639a72316343e8642","source":{"kind":"arxiv","id":"1802.06932","version":1},"attestation_state":"computed","paper":{"title":"Almost uniform and strong convergences in ergodic theorems for symmetric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Semyon Litvinov, Vladimir Chilin","submitted_at":"2018-02-20T01:45:25Z","abstract_excerpt":"Let $(\\Omega,\\mu)$ be a $\\sigma$-finite measure space, and let $X\\subset L^1(\\Omega)+L^\\infty(\\Omega)$ be a fully symmetric space of measurable functions on $(\\Omega,\\mu)$. If $\\mu(\\Omega)=\\infty$, necessary and sufficient conditions are given for almost uniform convergence in $X$ (in Egorov's sense) of Ces\\`aro averages $M_n(T)(f)=\\frac1n\\sum_{k = 0}^{n-1}T^k(f)$ for all Dunford-Schwartz operators $T$ in $L^1(\\Omega)+ L^\\infty(\\Omega)$ and any $f\\in X$. Besides, it is proved that the averages $M_n(T)$ converge strongly in $X$ for each Dunford-Schwartz operator $T$ in $L^1(\\Omega)+L^\\infty(\\Om"},"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":"1802.06932","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2018-02-20T01:45:25Z","cross_cats_sorted":[],"title_canon_sha256":"026ebf5a22eda563b2e8e5c60a0605343c21e0f7379df5e0d89fde563e19769b","abstract_canon_sha256":"c3faf98b93158587562ef3b7c5617465735bfead7b59b45ca09e93e2b64cb06d"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T00:22:53.955872Z","signature_b64":"Q6p+P6fc9jToQVX3eCDLO7IgJI1d+hCtbI62s/kdTje+l/K4m0MW8G5PfLtKdUn11Q/5cYyqwqE34V8paWDdDg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"665658774a559065c2ad7c5c1ac678c77aadc4117150e9a639a72316343e8642","last_reissued_at":"2026-05-18T00:22:53.955448Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T00:22:53.955448Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Almost uniform and strong convergences in ergodic theorems for symmetric spaces","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Semyon Litvinov, Vladimir Chilin","submitted_at":"2018-02-20T01:45:25Z","abstract_excerpt":"Let $(\\Omega,\\mu)$ be a $\\sigma$-finite measure space, and let $X\\subset L^1(\\Omega)+L^\\infty(\\Omega)$ be a fully symmetric space of measurable functions on $(\\Omega,\\mu)$. If $\\mu(\\Omega)=\\infty$, necessary and sufficient conditions are given for almost uniform convergence in $X$ (in Egorov's sense) of Ces\\`aro averages $M_n(T)(f)=\\frac1n\\sum_{k = 0}^{n-1}T^k(f)$ for all Dunford-Schwartz operators $T$ in $L^1(\\Omega)+ L^\\infty(\\Omega)$ and any $f\\in X$. Besides, it is proved that the averages $M_n(T)$ converge strongly in $X$ for each Dunford-Schwartz operator $T$ in $L^1(\\Omega)+L^\\infty(\\Om"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1802.06932","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":"1802.06932","created_at":"2026-05-18T00:22:53.955509+00:00"},{"alias_kind":"arxiv_version","alias_value":"1802.06932v1","created_at":"2026-05-18T00:22:53.955509+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1802.06932","created_at":"2026-05-18T00:22:53.955509+00:00"},{"alias_kind":"pith_short_12","alias_value":"MZLFQ52KKWIG","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_16","alias_value":"MZLFQ52KKWIGLQVN","created_at":"2026-05-18T12:32:40.477152+00:00"},{"alias_kind":"pith_short_8","alias_value":"MZLFQ52K","created_at":"2026-05-18T12:32:40.477152+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/MZLFQ52KKWIGLQVNPROBVRTYY5","json":"https://pith.science/pith/MZLFQ52KKWIGLQVNPROBVRTYY5.json","graph_json":"https://pith.science/api/pith-number/MZLFQ52KKWIGLQVNPROBVRTYY5/graph.json","events_json":"https://pith.science/api/pith-number/MZLFQ52KKWIGLQVNPROBVRTYY5/events.json","paper":"https://pith.science/paper/MZLFQ52K"},"agent_actions":{"view_html":"https://pith.science/pith/MZLFQ52KKWIGLQVNPROBVRTYY5","download_json":"https://pith.science/pith/MZLFQ52KKWIGLQVNPROBVRTYY5.json","view_paper":"https://pith.science/paper/MZLFQ52K","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1802.06932&json=true","fetch_graph":"https://pith.science/api/pith-number/MZLFQ52KKWIGLQVNPROBVRTYY5/graph.json","fetch_events":"https://pith.science/api/pith-number/MZLFQ52KKWIGLQVNPROBVRTYY5/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/MZLFQ52KKWIGLQVNPROBVRTYY5/action/timestamp_anchor","attest_storage":"https://pith.science/pith/MZLFQ52KKWIGLQVNPROBVRTYY5/action/storage_attestation","attest_author":"https://pith.science/pith/MZLFQ52KKWIGLQVNPROBVRTYY5/action/author_attestation","sign_citation":"https://pith.science/pith/MZLFQ52KKWIGLQVNPROBVRTYY5/action/citation_signature","submit_replication":"https://pith.science/pith/MZLFQ52KKWIGLQVNPROBVRTYY5/action/replication_record"}},"created_at":"2026-05-18T00:22:53.955509+00:00","updated_at":"2026-05-18T00:22:53.955509+00:00"}