{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2012:UDWP4BPVD5TFX6R5XUZ3OJ3QSA","short_pith_number":"pith:UDWP4BPV","schema_version":"1.0","canonical_sha256":"a0ecfe05f51f665bfa3dbd33b7277090155188ee66c61594cb42cd0ce4ee832e","source":{"kind":"arxiv","id":"1208.4272","version":2},"attestation_state":"computed","paper":{"title":"Higher moments of Banach space valued random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Sten Kaijser, Svante Janson","submitted_at":"2012-08-21T14:12:30Z","abstract_excerpt":"We define the $k$:th moment of a Banach space valued random variable as the expectation of its $k$:th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space.\n  We study both the projective and injective tensor products, and their relation. Moreover, in order to be general and flexible, we study three different types of expectations: Bochner integrals, Pettis integrals and Dunford integrals.\n  One of the problems studied is whether two random variables with the same injective moments (of a given order) necessarily have the same projective momen"},"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":"1208.4272","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.PR","submitted_at":"2012-08-21T14:12:30Z","cross_cats_sorted":["math.FA"],"title_canon_sha256":"b01c1be80f4643a7b6babad31eef112fa1fcdf91274a21110e2cd6080007be29","abstract_canon_sha256":"5a19ba22c71fa58f05b7f6a34bd12a59a6bf3300d0e022a046b8bf2b20ebe17f"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-18T03:46:46.837984Z","signature_b64":"P8cKDB2yyje607xJw61jr/mGL4xmASAt772ZIjwkn8cDOn1+NtPjK6GgS/+lkYhvQUPElULaDzeskPwmwj0tAw==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"a0ecfe05f51f665bfa3dbd33b7277090155188ee66c61594cb42cd0ce4ee832e","last_reissued_at":"2026-05-18T03:46:46.837110Z","signature_status":"signed_v1","first_computed_at":"2026-05-18T03:46:46.837110Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Higher moments of Banach space valued random variables","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":["math.FA"],"primary_cat":"math.PR","authors_text":"Sten Kaijser, Svante Janson","submitted_at":"2012-08-21T14:12:30Z","abstract_excerpt":"We define the $k$:th moment of a Banach space valued random variable as the expectation of its $k$:th tensor power; thus the moment (if it exists) is an element of a tensor power of the original Banach space.\n  We study both the projective and injective tensor products, and their relation. Moreover, in order to be general and flexible, we study three different types of expectations: Bochner integrals, Pettis integrals and Dunford integrals.\n  One of the problems studied is whether two random variables with the same injective moments (of a given order) necessarily have the same projective momen"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1208.4272","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":"1208.4272","created_at":"2026-05-18T03:46:46.837253+00:00"},{"alias_kind":"arxiv_version","alias_value":"1208.4272v2","created_at":"2026-05-18T03:46:46.837253+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1208.4272","created_at":"2026-05-18T03:46:46.837253+00:00"},{"alias_kind":"pith_short_12","alias_value":"UDWP4BPVD5TF","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_16","alias_value":"UDWP4BPVD5TFX6R5","created_at":"2026-05-18T12:27:23.164592+00:00"},{"alias_kind":"pith_short_8","alias_value":"UDWP4BPV","created_at":"2026-05-18T12:27:23.164592+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/UDWP4BPVD5TFX6R5XUZ3OJ3QSA","json":"https://pith.science/pith/UDWP4BPVD5TFX6R5XUZ3OJ3QSA.json","graph_json":"https://pith.science/api/pith-number/UDWP4BPVD5TFX6R5XUZ3OJ3QSA/graph.json","events_json":"https://pith.science/api/pith-number/UDWP4BPVD5TFX6R5XUZ3OJ3QSA/events.json","paper":"https://pith.science/paper/UDWP4BPV"},"agent_actions":{"view_html":"https://pith.science/pith/UDWP4BPVD5TFX6R5XUZ3OJ3QSA","download_json":"https://pith.science/pith/UDWP4BPVD5TFX6R5XUZ3OJ3QSA.json","view_paper":"https://pith.science/paper/UDWP4BPV","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1208.4272&json=true","fetch_graph":"https://pith.science/api/pith-number/UDWP4BPVD5TFX6R5XUZ3OJ3QSA/graph.json","fetch_events":"https://pith.science/api/pith-number/UDWP4BPVD5TFX6R5XUZ3OJ3QSA/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/UDWP4BPVD5TFX6R5XUZ3OJ3QSA/action/timestamp_anchor","attest_storage":"https://pith.science/pith/UDWP4BPVD5TFX6R5XUZ3OJ3QSA/action/storage_attestation","attest_author":"https://pith.science/pith/UDWP4BPVD5TFX6R5XUZ3OJ3QSA/action/author_attestation","sign_citation":"https://pith.science/pith/UDWP4BPVD5TFX6R5XUZ3OJ3QSA/action/citation_signature","submit_replication":"https://pith.science/pith/UDWP4BPVD5TFX6R5XUZ3OJ3QSA/action/replication_record"}},"created_at":"2026-05-18T03:46:46.837253+00:00","updated_at":"2026-05-18T03:46:46.837253+00:00"}