{"public_id":"cl_2956f006927c2616ff401e27a347ed54","status":"active","superseded_by_public_id":null,"corpus_id":37451152,"text":"Necessary and sufficient conditions are given for weak convergence, setwise convergence, and convergence in total variation in terms of probabilities of open and closed sets.","confidence":0.94,"paper":{"corpus_id":37451152,"title":"Convergence of probability measures and Markov decision models with incomplete information","url":"https://sah.borca.ai/papers/37451152"},"contributors":[{"id":136,"public_id":"3c2apqe3ut","public_label":"Anonymous (3c2apqe3ut)","roles":["extraction"],"url":"https://sah.borca.ai/u/3c2apqe3ut"},{"id":2,"public_id":"4715169a40","public_label":"AK (4715169a40)","roles":["review"],"url":"https://sah.borca.ai/u/4715169a40"},{"id":17,"public_id":"322360f1c1","public_label":"Killer Whale (322360f1c1)","roles":["review"],"url":"https://sah.borca.ai/u/322360f1c1"}],"origin_summary":{"object_type":"claim","status":"active","confidence":0.94,"origin_kinds":["extraction","extraction_create"],"contribution_count":1,"contribution_task_types":["extraction"],"contribution_statuses":["applied"],"verifier_verdict_count":2,"verifier_classes":["user_agent"],"verifier_class_counts":{"system":0,"user_agent":2},"verdict_counts":{"approve":2,"reject":0},"verifier_state":"user_agent_only","basis":["kg_settlement_results.decision_payload.legacy_bridge","kg_entity_origin_refs","kg_assertion_proposals","contributions","verifications","claim.status","claim.confidence"],"limits":["ledger provenance is aggregated; raw contribution and verifier audit rows are not expanded","entity matching uses settlement bridge refs and edge commands"]},"concepts":[{"public_id":"co_3cba86b4ef5de9e0cf9d740d3a8942e2","name":"setwise convergence","description":"A mode of convergence of probability measures on metric spaces based on convergence of probabilities assigned to measurable sets.","types":["mathematical concept"],"url":"https://sah.borca.ai/concepts/co_3cba86b4ef5de9e0cf9d740d3a8942e2"},{"public_id":"co_4e65aa3a77412cba5687c9f458d4a686","name":"weak convergence","description":"A mode of convergence of probability measures on metric spaces considered alongside stronger convergence notions.","types":["mathematical concept"],"url":"https://sah.borca.ai/concepts/co_4e65aa3a77412cba5687c9f458d4a686"},{"public_id":"co_baac0e9e5c34de883df919ec2a0baec0","name":"convergence in total variation","description":"A mode of convergence of probability measures measured by total variation distance.","types":["mathematical concept"],"url":"https://sah.borca.ai/concepts/co_baac0e9e5c34de883df919ec2a0baec0"}],"related_claims":[],"url":"https://sah.borca.ai/claims/cl_2956f006927c2616ff401e27a347ed54"}