{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:YTVGZOBBJJDN3B2XZWY5WC7K72","short_pith_number":"pith:YTVGZOBB","schema_version":"1.0","canonical_sha256":"c4ea6cb8214a46dd8757cdb1db0beafea8a0560c44846c95e6bc51806a550d4f","source":{"kind":"arxiv","id":"1203.5191","version":1},"attestation_state":"computed","paper":{"title":"On the convergence of double integrals and a generalized version of Fubini's theorem on successive integration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ferenc Moricz","submitted_at":"2012-03-23T07:25:36Z","abstract_excerpt":"Let the function $f: \\bar{\\R}^2_+ \\to \\C$ be such that $f\\in L^1_{\\loc} (\\bar{\\R}^2_+)$. We investigate the convergence behavior of the double integral $$\\int^A_0 \\int^B_0 f(u,v) du dv \\quad {\\rm as} \\quad A,B \\to \\infty,\\leqno(*)$$ where $A$ and $B$ tend to infinity independently of one another; while using two notions of convergence: that in Pringsheim's sense and that in the regular sense. Our main result is the following Theorem 3: If the double integral (*) converges in the regular sense, or briefly: converges regularly, then the finite limits $$\\lim_{y\\to \\infty} \\int^A_0 \\Big(\\int^y_0 f"},"verification_status":{"content_addressed":true,"pith_receipt":true,"author_attested":false,"weak_author_claims":0,"strong_author_claims":0,"externally_anchored":false,"storage_verified":false,"citation_signatures":0,"replication_records":0,"graph_snapshot":true,"references_resolved":false,"formal_links_present":false},"canonical_record":{"source":{"id":"1203.5191","kind":"arxiv","version":1},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.CA","submitted_at":"2012-03-23T07:25:36Z","cross_cats_sorted":[],"title_canon_sha256":"dee056fa745aaaccb6677de9275163ec5b654452ae384b5cea56730d67541bbe","abstract_canon_sha256":"5bfed1205f7db5689e6f1fa1636ef5256609924b32c3667aa1f71d9d816dbe62"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:59:26.628175Z","signature_b64":"tc2jlzVkIZ99SteZ0LtheVtaUEhG6Q2B4EqYgjymTqVQqSdFvehNBlcY+KGSASzzn1uGsonrmQjAf9OyohqACg==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"c4ea6cb8214a46dd8757cdb1db0beafea8a0560c44846c95e6bc51806a550d4f","last_reissued_at":"2026-05-18T03:59:26.627462Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:59:26.627462Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"On the convergence of double integrals and a generalized version of Fubini's theorem on successive integration","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.CA","authors_text":"Ferenc Moricz","submitted_at":"2012-03-23T07:25:36Z","abstract_excerpt":"Let the function $f: \\bar{\\R}^2_+ \\to \\C$ be such that $f\\in L^1_{\\loc} (\\bar{\\R}^2_+)$. We investigate the convergence behavior of the double integral $$\\int^A_0 \\int^B_0 f(u,v) du dv \\quad {\\rm as} \\quad A,B \\to \\infty,\\leqno(*)$$ where $A$ and $B$ tend to infinity independently of one another; while using two notions of convergence: that in Pringsheim's sense and that in the regular sense. Our main result is the following Theorem 3: If the double integral (*) converges in the regular sense, or briefly: converges regularly, then the finite limits $$\\lim_{y\\to \\infty} \\int^A_0 \\Big(\\int^y_0 f"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1203.5191","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":"1203.5191","created_at":"2026-05-18T03:59:26.627576+00:00"},{"alias_kind":"arxiv_version","alias_value":"1203.5191v1","created_at":"2026-05-18T03:59:26.627576+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1203.5191","created_at":"2026-05-18T03:59:26.627576+00:00"},{"alias_kind":"pith_short_12","alias_value":"YTVGZOBBJJDN","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_16","alias_value":"YTVGZOBBJJDN3B2X","created_at":"2026-05-18T12:27:30.460161+00:00"},{"alias_kind":"pith_short_8","alias_value":"YTVGZOBB","created_at":"2026-05-18T12:27:30.460161+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/YTVGZOBBJJDN3B2XZWY5WC7K72","json":"https://pith.science/pith/YTVGZOBBJJDN3B2XZWY5WC7K72.json","graph_json":"https://pith.science/api/pith-number/YTVGZOBBJJDN3B2XZWY5WC7K72/graph.json","events_json":"https://pith.science/api/pith-number/YTVGZOBBJJDN3B2XZWY5WC7K72/events.json","paper":"https://pith.science/paper/YTVGZOBB"},"agent_actions":{"view_html":"https://pith.science/pith/YTVGZOBBJJDN3B2XZWY5WC7K72","download_json":"https://pith.science/pith/YTVGZOBBJJDN3B2XZWY5WC7K72.json","view_paper":"https://pith.science/paper/YTVGZOBB","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1203.5191&json=true","fetch_graph":"https://pith.science/api/pith-number/YTVGZOBBJJDN3B2XZWY5WC7K72/graph.json","fetch_events":"https://pith.science/api/pith-number/YTVGZOBBJJDN3B2XZWY5WC7K72/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/YTVGZOBBJJDN3B2XZWY5WC7K72/action/timestamp_anchor","attest_storage":"https://pith.science/pith/YTVGZOBBJJDN3B2XZWY5WC7K72/action/storage_attestation","attest_author":"https://pith.science/pith/YTVGZOBBJJDN3B2XZWY5WC7K72/action/author_attestation","sign_citation":"https://pith.science/pith/YTVGZOBBJJDN3B2XZWY5WC7K72/action/citation_signature","submit_replication":"https://pith.science/pith/YTVGZOBBJJDN3B2XZWY5WC7K72/action/replication_record"}},"created_at":"2026-05-18T03:59:26.627576+00:00","updated_at":"2026-05-18T03:59:26.627576+00:00"}