{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:1994:ZGTS2R4PWX4BQ5ZQW67MM5DVMI","short_pith_number":"pith:ZGTS2R4P","schema_version":"1.0","canonical_sha256":"c9a72d478fb5f8187730b7bec67475620e6b66001ad6effdc0b9319c9d7927c9","source":{"kind":"arxiv","id":"math/9412211","version":1},"attestation_state":"computed","paper":{"title":"On Convergence of Conditional Expectation Operators","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"C. Bryan Dawson","submitted_at":"1994-12-05T17:46:25Z","abstract_excerpt":"Given an operator $T:U_X(\\Sigma)\\to Y$ or ${T:U(\\Sigma)\\to Y$, one may consider the net of conditional expectation operators $(T_\\pi)$ directed by refinement of the partitions $\\pi$. It has been shown previously that $(T_\\pi)$ does not always converge to $T$. This paper gives several conditions under which this convergence does occur, including complete characterizations when $X={\\bold R}$ or when $X\\sp *$ has the Radon-Nikod\\'ym property."},"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":"math/9412211","kind":"arxiv","version":1},"metadata":{"license":"","primary_cat":"math.FA","submitted_at":"1994-12-05T17:46:25Z","cross_cats_sorted":[],"title_canon_sha256":"8be28f407ff4a31cf63a6cce973a104c6e219d081ac3ae9500e98fa7a4c66a8a","abstract_canon_sha256":"8da539d8d5cdb6780886b23dbb0d2f68748998c70e5974f084b3b61379c78dd5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:05:50.769009Z","signature_b64":"MrrRjq+TAtyxJcBbiWxQqqTK8TfObjRw+QsJ+4+qPzxYvoP6TTDY9hP9Zs25IisoeI+q513dv8XvQ0VtjtCiAA==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c9a72d478fb5f8187730b7bec67475620e6b66001ad6effdc0b9319c9d7927c9","last_reissued_at":"2026-05-18T01:05:50.768404Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:05:50.768404Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On Convergence of Conditional Expectation Operators","license":"","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"C. Bryan Dawson","submitted_at":"1994-12-05T17:46:25Z","abstract_excerpt":"Given an operator $T:U_X(\\Sigma)\\to Y$ or ${T:U(\\Sigma)\\to Y$, one may consider the net of conditional expectation operators $(T_\\pi)$ directed by refinement of the partitions $\\pi$. It has been shown previously that $(T_\\pi)$ does not always converge to $T$. This paper gives several conditions under which this convergence does occur, including complete characterizations when $X={\\bold R}$ or when $X\\sp *$ has the Radon-Nikod\\'ym property."},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"math/9412211","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":"math/9412211","created_at":"2026-05-18T01:05:50.768496+00:00"},{"alias_kind":"arxiv_version","alias_value":"math/9412211v1","created_at":"2026-05-18T01:05:50.768496+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.math/9412211","created_at":"2026-05-18T01:05:50.768496+00:00"},{"alias_kind":"pith_short_12","alias_value":"ZGTS2R4PWX4B","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_16","alias_value":"ZGTS2R4PWX4BQ5ZQ","created_at":"2026-05-18T12:25:47.102015+00:00"},{"alias_kind":"pith_short_8","alias_value":"ZGTS2R4P","created_at":"2026-05-18T12:25:47.102015+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/ZGTS2R4PWX4BQ5ZQW67MM5DVMI","json":"https://pith.science/pith/ZGTS2R4PWX4BQ5ZQW67MM5DVMI.json","graph_json":"https://pith.science/api/pith-number/ZGTS2R4PWX4BQ5ZQW67MM5DVMI/graph.json","events_json":"https://pith.science/api/pith-number/ZGTS2R4PWX4BQ5ZQW67MM5DVMI/events.json","paper":"https://pith.science/paper/ZGTS2R4P"},"agent_actions":{"view_html":"https://pith.science/pith/ZGTS2R4PWX4BQ5ZQW67MM5DVMI","download_json":"https://pith.science/pith/ZGTS2R4PWX4BQ5ZQW67MM5DVMI.json","view_paper":"https://pith.science/paper/ZGTS2R4P","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=math/9412211&json=true","fetch_graph":"https://pith.science/api/pith-number/ZGTS2R4PWX4BQ5ZQW67MM5DVMI/graph.json","fetch_events":"https://pith.science/api/pith-number/ZGTS2R4PWX4BQ5ZQW67MM5DVMI/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/ZGTS2R4PWX4BQ5ZQW67MM5DVMI/action/timestamp_anchor","attest_storage":"https://pith.science/pith/ZGTS2R4PWX4BQ5ZQW67MM5DVMI/action/storage_attestation","attest_author":"https://pith.science/pith/ZGTS2R4PWX4BQ5ZQW67MM5DVMI/action/author_attestation","sign_citation":"https://pith.science/pith/ZGTS2R4PWX4BQ5ZQW67MM5DVMI/action/citation_signature","submit_replication":"https://pith.science/pith/ZGTS2R4PWX4BQ5ZQW67MM5DVMI/action/replication_record"}},"created_at":"2026-05-18T01:05:50.768496+00:00","updated_at":"2026-05-18T01:05:50.768496+00:00"}