{"id":"W3161721067","doi":"10.21203/rs.3.rs-509111/v1","title":"Bicomplex Version of Lebesgue's Dominated Convergence Theorem and Hyperbolic Invariant Measure","year":2021,"lang":"en","type":"preprint","venue":"Research Square","topic":"Mathematical Dynamics and Fractals","field":"Mathematics","cited_by":0,"is_retracted":false,"has_abstract":true,"ca_institutions":"Adidas (Canada)","funders":"","keywords":"Lebesgue integration; Dominated convergence theorem; Lebesgue measure; Mathematics; Invariant (physics); Lebesgue–Stieltjes integration; Standard probability space; Pure mathematics; Lp space; Measurable function; Measure (data warehouse); Convergence (economics); Discrete mathematics; Riemann integral; Mathematical analysis; Rate of convergence; Banach space; Convergence tests; Computer science; Key (lock)","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":"metacan-v3-hybrid-931329e0061c","candidate_categories":[],"consensus_categories":[],"category_scores_codex":[0.00118812,0.0003673461,0.0006431999,0.001818022,0.0006315401,0.002343973,0.0006238106,0.00033505,0.004628954],"category_scores_gemma":[0.001921413,0.0001512304,0.0003415699,0.0009030948,0.001692656,0.002115281,0.001657125,0.001121799,0.0004174859],"about_ca_system_candidate":false,"about_ca_system_consensus":false,"about_ca_system_score_codex":0.001217062,"about_ca_system_score_gemma":0.0003471399,"about_ca_topic_candidate":false,"about_ca_topic_consensus":false,"about_ca_topic_score_codex":0.001030062,"about_ca_topic_score_gemma":0.000541495,"domain_scores_codex":[0.9992685,0.0001353969,0.00003440972,0.0001269653,0.0003351712,0.00009950801],"domain_scores_gemma":[0.9984505,0.0003632772,0.0002341149,0.0001454664,0.0006063507,0.0002003238],"domain_codex":null,"domain_gemma":null,"domain_candidate":null,"domain_consensus":null,"study_design_codex":"theoretical_or_conceptual","study_design_gemma":"theoretical_or_conceptual","study_design_scores_codex":[0.00003214711,0.00001412894,0.001067604,0.000057008,0.00001276866,0.0001709683,0.0002285515,0.002528192,0.003021838,0.9863403,0.0007064015,0.005820198],"study_design_scores_gemma":[0.00002042688,0.00009363552,0.004481951,0.00003192285,0.00001281918,0.0006329479,0.0004493419,0.04308491,0.003713887,0.9345016,0.01294866,0.00002777255],"study_design_candidate":"theoretical_or_conceptual","study_design_consensus":"theoretical_or_conceptual","genre_codex":"empirical","genre_gemma":"empirical","genre_scores_codex":[0.5185189,0.002377232,0.385582,0.001657538,0.0002094081,0.00005432848,0.0004753293,0.0001605611,0.09096473],"genre_scores_gemma":[0.972081,0.0004597023,0.01227675,0.0002230059,0.00009237295,0.00004189336,0.0001670955,0.00003913085,0.01461902],"genre_candidate":"empirical","genre_consensus":"empirical","teacher_disagreement_score":0.004628954,"threshold_uncertainty_score":0.01548541,"prediction_status":"machine_predicted_unvalidated"},"machine_scores":{"provisional":true,"baseline":true,"maturity_gate_passed":false,"score_opus":0.1108230364591108,"score_gpt":0.3958654594931437,"score_spread":0.2850424230340329,"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."}}