{"record_type":"pith_number_record","schema_url":"https://pith.science/schemas/pith-number/v1.json","pith_number":"pith:2019:26EIVZ6AR33L4XOT3YN7OQ7TMQ","short_pith_number":"pith:26EIVZ6A","schema_version":"1.0","canonical_sha256":"d7888ae7c08ef6be5dd3de1bf743f3642e64329f0a8a5a3ab008fac151b09541","source":{"kind":"arxiv","id":"1904.03642","version":2},"attestation_state":"computed","paper":{"title":"Kantorovich problems and conditional measures depending on a parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Il'ya Malofeev, Vladimir Bogachev","submitted_at":"2019-04-07T12:52:05Z","abstract_excerpt":"We study measurable dependence of measures on a parameter in the following two classical problems: constructing conditional measures and the Kantorovich optimal transportation. We obtain broad sufficient conditions for the existence of conditional probabilities measurably depending on a parameter in the case of parametric families of measures and mappings. A~particular emphasis is made on the Borel measurability (which cannot be always achieved). Our second main result gives sufficient conditions for the Borel measurability of optimal transports and transportation costs with respect to a param"},"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":"1904.03642","kind":"arxiv","version":2},"metadata":{"license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","primary_cat":"math.FA","submitted_at":"2019-04-07T12:52:05Z","cross_cats_sorted":[],"title_canon_sha256":"4d6648e98d8074bd431b9d9aac4be55a7534cb97cfce21b1d24aa22ae0642648","abstract_canon_sha256":"5c3381448554c7ecb6755fb757a568259a02e4beeff4a15c821d4a0a587d504e"},"schema_version":"1.0"},"receipt":{"kind":"pith_receipt","key_id":"pith-v1-2026-05","algorithm":"ed25519","signed_at":"2026-05-17T23:41:36.386065Z","signature_b64":"aWrklRBuDHWuOSXd9nFdZNR9oTlynOebhKgQo4blnbWZUnF/rRaNyjVYjlP+PSYlTCwZZL9AoJGAODOn8+nkBQ==","signed_message":"canonical_sha256_bytes","builder_version":"pith-number-builder-2026-05-17-v1","receipt_version":"0.3","canonical_sha256":"d7888ae7c08ef6be5dd3de1bf743f3642e64329f0a8a5a3ab008fac151b09541","last_reissued_at":"2026-05-17T23:41:36.385375Z","signature_status":"signed_v1","first_computed_at":"2026-05-17T23:41:36.385375Z","public_key_fingerprint":"8d4b5ee74e4693bcd1df2446408b0d54"},"graph_snapshot":{"paper":{"title":"Kantorovich problems and conditional measures depending on a parameter","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.FA","authors_text":"Il'ya Malofeev, Vladimir Bogachev","submitted_at":"2019-04-07T12:52:05Z","abstract_excerpt":"We study measurable dependence of measures on a parameter in the following two classical problems: constructing conditional measures and the Kantorovich optimal transportation. We obtain broad sufficient conditions for the existence of conditional probabilities measurably depending on a parameter in the case of parametric families of measures and mappings. A~particular emphasis is made on the Borel measurability (which cannot be always achieved). Our second main result gives sufficient conditions for the Borel measurability of optimal transports and transportation costs with respect to a param"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1904.03642","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":"1904.03642","created_at":"2026-05-17T23:41:36.385490+00:00"},{"alias_kind":"arxiv_version","alias_value":"1904.03642v2","created_at":"2026-05-17T23:41:36.385490+00:00"},{"alias_kind":"doi","alias_value":"10.48550/arxiv.1904.03642","created_at":"2026-05-17T23:41:36.385490+00:00"},{"alias_kind":"pith_short_12","alias_value":"26EIVZ6AR33L","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_16","alias_value":"26EIVZ6AR33L4XOT","created_at":"2026-05-18T12:33:07.085635+00:00"},{"alias_kind":"pith_short_8","alias_value":"26EIVZ6A","created_at":"2026-05-18T12:33:07.085635+00:00"}],"events":[],"event_summary":{},"paper_claims":[],"inbound_citations":{"count":1,"internal_anchor_count":1,"sample":[{"citing_arxiv_id":"1908.07021","citing_title":"A synthetic approach to Markov kernels, conditional independence and theorems on sufficient statistics","ref_index":8,"is_internal_anchor":true}]},"formal_canon":{"evidence_count":0,"sample":[],"anchors":[]},"links":{"html":"https://pith.science/pith/26EIVZ6AR33L4XOT3YN7OQ7TMQ","json":"https://pith.science/pith/26EIVZ6AR33L4XOT3YN7OQ7TMQ.json","graph_json":"https://pith.science/api/pith-number/26EIVZ6AR33L4XOT3YN7OQ7TMQ/graph.json","events_json":"https://pith.science/api/pith-number/26EIVZ6AR33L4XOT3YN7OQ7TMQ/events.json","paper":"https://pith.science/paper/26EIVZ6A"},"agent_actions":{"view_html":"https://pith.science/pith/26EIVZ6AR33L4XOT3YN7OQ7TMQ","download_json":"https://pith.science/pith/26EIVZ6AR33L4XOT3YN7OQ7TMQ.json","view_paper":"https://pith.science/paper/26EIVZ6A","resolve_alias":"https://pith.science/api/pith-number/resolve?arxiv=1904.03642&json=true","fetch_graph":"https://pith.science/api/pith-number/26EIVZ6AR33L4XOT3YN7OQ7TMQ/graph.json","fetch_events":"https://pith.science/api/pith-number/26EIVZ6AR33L4XOT3YN7OQ7TMQ/events.json","actions":{"anchor_timestamp":"https://pith.science/pith/26EIVZ6AR33L4XOT3YN7OQ7TMQ/action/timestamp_anchor","attest_storage":"https://pith.science/pith/26EIVZ6AR33L4XOT3YN7OQ7TMQ/action/storage_attestation","attest_author":"https://pith.science/pith/26EIVZ6AR33L4XOT3YN7OQ7TMQ/action/author_attestation","sign_citation":"https://pith.science/pith/26EIVZ6AR33L4XOT3YN7OQ7TMQ/action/citation_signature","submit_replication":"https://pith.science/pith/26EIVZ6AR33L4XOT3YN7OQ7TMQ/action/replication_record"}},"created_at":"2026-05-17T23:41:36.385490+00:00","updated_at":"2026-05-17T23:41:36.385490+00:00"}