0506950 20240103222330.520190726235959.9 84941882338 000362310900009 10.1214/14-BJPS251 19 s. P cav_un_epca*03324250103-0752294 (2015)878-896 Capacities probability inequalities Choquet-like expectation cav_un_auth*0261431 40 Agahi H. IR K cav_un_auth*0283606 30 Mohammadpour A. IR cav_un_auth*0101163 Ekonometrie Department of Econometrics E E Department of Econometrics 30 Mesiar Radko UTIA-B Ústav teorie informace a automatizace AV ČR, v. v. i. http://library.utia.cas.cz/separaty/2019/E/mesiar-0506950.pdf This paper has three specific aims. First, some probability inequal-ities, including Hölder’s inequality, Lyapunov’s inequality, Minkowski’s in-equality, concentration inequalities and Fatou’s lemma for Choquet-like ex-pectation based on a monotone measure are shown, extending previous workof many researchers. Second, we generalize some theorems about the con-vergence of sequences of random variables on monotone measure spaces forChoquet-like expectation. Third, we extend the concept of uniform integra-bility for Choquet-like expectation. These results are useful for the solutionof various problems in machine learning and made it possible to derive newefficient algorithms in any monotone system. Corresponding results are validfor capacities, the usefulness of which has been demonstrated by the rapidlyexpanding literature on generalized probability theory. WOS BA 10000 10100 10103 2020 3 RVO:67985556 http://hdl.handle.net/11104/0298083 S STATISTICS&PROBABILITY 0.432 0.051 0.00087 0.392 92 0.377 Q3 0.377 39 Q4 16.306 12.6 Q4 Q4 12.602 2015 84941882338 SCOPUS PUBMED 000362310900009 WOS cav_un_epca*0332425 Brazilian Journal of Probability and Statistics 0103-0752 0103-0752 Roč. 29 č. 4 2015 878 896