{"id":"W2167163902","doi":"10.1016/s0167-7152(00)00146-2","title":"Convergence of randomly weighted sums of Banach space valued random elements and uniform integrability concerning the random weights","year":2001,"lang":"en","type":"article","venue":"Statistics & Probability Letters","topic":"Probability and Risk Models","field":"Decision Sciences","cited_by":18,"is_retracted":false,"has_abstract":false,"ca_institutions":"University of Regina","funders":"","keywords":"Mathematics; Banach space; Separable space; Convergence of random variables; Sequence (biology); Convergence (economics); Law of large numbers; Weak convergence; Random variable; Conditional expectation; Random element; Space (punctuation); Order (exchange); Unconditional convergence; Discrete mathematics; Pure mathematics; Applied mathematics; Mathematical analysis; Compact convergence; Statistics; Rate of convergence","routes":{"ca_aff":true,"ca_fund":false,"ca_venue":false,"about_ca":false,"invisible_to_affiliation_only":false},"retraction":null,"screen":null,"direct_labels":[],"prediction":{"model_version":"codex-gemma-dda1882f352a","candidate_categories":["metaepi_narrow","sts"],"consensus_categories":[],"category_scores_codex":[0.01361681,0.0004172978,0.001322529,0.0001763883,0.0003647232,0.00011127,0.001186975,0.0001439872,0.0004767262],"category_scores_gemma":[0.008105632,0.0002467735,0.0002797238,0.0008887186,0.003069937,0.0003806346,0.0003033902,0.0004671183,0.00001488215],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.0001269177,"about_ca_system_score_gemma":0.0002348246,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.0007194879,"about_ca_topic_score_gemma":0.0005059564,"domain_scores_codex":[0.9917626,0.002042858,0.002617799,0.001010435,0.001978696,0.0005876346],"domain_scores_gemma":[0.9867416,0.009238055,0.001201604,0.001503577,0.001106207,0.0002089803],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"observational","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.02108621,0.0008411467,0.69786,0.0006086591,0.0006068135,0.00001993906,0.01289582,0.0005385274,0.00653126,0.2297641,0.005536894,0.0237106],"study_design_scores_gemma":[0.01581504,0.000233317,0.02383105,0.00009244195,0.0001992411,0.000008467112,0.0002020186,0.03853422,0.002566109,0.9163901,0.001670815,0.0004571853],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":null,"genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.579443,0.0001522532,0.4166651,0.001664896,0.0002399077,0.001360029,0.0002625219,0.00002292264,0.0001893096],"genre_scores_gemma":[0.9294397,0.0001187319,0.06996872,0.0002213552,0.00003632757,0.00005528473,0.00002618017,0.00001778663,0.000115947],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.686626,"threshold_uncertainty_score":0.9999985,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.0601172159550851,"score_gpt":0.3185135312764436,"score_spread":0.2583963153213584,"validation_status":"score_only:v0-immature-baseline","note":"Baseline scores from an immature model (maturity gate not passed). Scores rank; they never assert a category."}}