{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2016:GM2QVZQFD6VKT3QMZI7JLVZEWE","short_pith_number":"pith:GM2QVZQF","schema_version":"1.0","canonical_sha256":"33350ae6051faaa9ee0cca3e95d724b10ba89d814fa264221dabfd959307fae7","source":{"kind":"arxiv","id":"1605.05434","version":2},"attestation_state":"computed","paper":{"title":"A Note on Uniform Nonintegrability of Random Variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Xue Peng, Ze-Chun Hu","submitted_at":"2016-05-18T04:19:20Z","abstract_excerpt":"In a recent paper \\cite{CHR16}, Chandra, Hu and Rosalsky introduced the notion of a sequence of random variables being uniformly nonintegrable, and presented a list of interesting results on this uniform nonintegrability. In this note, we introduce a weaker definition on uniform nonintegrability (W-UNI for short) of random variables, present a necessary and sufficient condition for W-UNI, and give two equivalent characterizations of W-UNI, one of which is a W-UNI analogue of the celebrated de La Vall\\'{e}e Poussin criterion for uniform integrability. In addition, we give some remarks, one of w"},"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":"1605.05434","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2016-05-18T04:19:20Z","cross_cats_sorted":[],"title_canon_sha256":"44347b21f66b2c112e8d80c411e62e2949799cca577f509603fefff578b24ddc","abstract_canon_sha256":"5ba6d50bdee23cfedee534ecb6c0127ea73743e1ff24c473b8324894b0844fe5"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T01:12:48.220051Z","signature_b64":"l071+EYYDDL6c2+4kEAoQpZcuPk32hNErwYElkz8/A9m/ZOpDtqMDf9wh++i31gkMo1uS5cim6E+lMjc7QLUAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"33350ae6051faaa9ee0cca3e95d724b10ba89d814fa264221dabfd959307fae7","last_reissued_at":"2026-05-18T01:12:48.219686Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T01:12:48.219686Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"A Note on Uniform Nonintegrability of Random Variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.PR","authors_text":"Xue Peng, Ze-Chun Hu","submitted_at":"2016-05-18T04:19:20Z","abstract_excerpt":"In a recent paper \\cite{CHR16}, Chandra, Hu and Rosalsky introduced the notion of a sequence of random variables being uniformly nonintegrable, and presented a list of interesting results on this uniform nonintegrability. In this note, we introduce a weaker definition on uniform nonintegrability (W-UNI for short) of random variables, present a necessary and sufficient condition for W-UNI, and give two equivalent characterizations of W-UNI, one of which is a W-UNI analogue of the celebrated de La Vall\\'{e}e Poussin criterion for uniform integrability. In addition, we give some remarks, one of w"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1605.05434","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"},"aliases":[{"alias_kind":"arxiv","alias_value":"1605.05434","created_at":"2026-05-18T01:12:48.219740+00:00"},{"alias_kind":"arxiv_version","alias_value":"1605.05434v2","created_at":"2026-05-18T01:12:48.219740+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1605.05434","created_at":"2026-05-18T01:12:48.219740+00:00"},{"alias_kind":"pith_short_12","alias_value":"GM2QVZQFD6VK","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_16","alias_value":"GM2QVZQFD6VKT3QM","created_at":"2026-05-18T12:30:19.053100+00:00"},{"alias_kind":"pith_short_8","alias_value":"GM2QVZQF","created_at":"2026-05-18T12:30:19.053100+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/GM2QVZQFD6VKT3QMZI7JLVZEWE","json":"https://pith.science/pith/GM2QVZQFD6VKT3QMZI7JLVZEWE.json","graph_json":"https://pith.science/api/pith-number/GM2QVZQFD6VKT3QMZI7JLVZEWE/graph.json","events_json":"https://pith.science/api/pith-number/GM2QVZQFD6VKT3QMZI7JLVZEWE/events.json","paper":"https://pith.science/paper/GM2QVZQF"},"agent_actions":{"view_html":"https://pith.science/pith/GM2QVZQFD6VKT3QMZI7JLVZEWE","download_json":"https://pith.science/pith/GM2QVZQFD6VKT3QMZI7JLVZEWE.json","view_paper":"https://pith.science/paper/GM2QVZQF","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1605.05434&json=true","fetch_graph":"https://pith.science/api/pith-number/GM2QVZQFD6VKT3QMZI7JLVZEWE/graph.json","fetch_events":"https://pith.science/api/pith-number/GM2QVZQFD6VKT3QMZI7JLVZEWE/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/GM2QVZQFD6VKT3QMZI7JLVZEWE/action/timestamp_anchor","attest_storage":"https://pith.science/pith/GM2QVZQFD6VKT3QMZI7JLVZEWE/action/storage_attestation","attest_author":"https://pith.science/pith/GM2QVZQFD6VKT3QMZI7JLVZEWE/action/author_attestation","sign_citation":"https://pith.science/pith/GM2QVZQFD6VKT3QMZI7JLVZEWE/action/citation_signature","submit_replication":"https://pith.science/pith/GM2QVZQFD6VKT3QMZI7JLVZEWE/action/replication_record"}},"created_at":"2026-05-18T01:12:48.219740+00:00","updated_at":"2026-05-18T01:12:48.219740+00:00"}