期刊名称：Brazilian Journal of Probability and Statistics
印刷版ISSN：0103-0752
出版年度：2015
卷号：29
期号：4
页码：878-896
DOI：10.1214/14-BJPS251
语种：English
出版社：Brazilian Statistical Association
摘要：This paper has three specific aims. First, some probability inequalities, including Hölder’s inequality, Lyapunov’s inequality, Minkowski’s inequality, concentration inequalities and Fatou’s lemma for Choquet-like expectation based on a monotone measure are shown, extending previous work of many researchers. Second, we generalize some theorems about the convergence of sequences of random variables on monotone measure spaces for Choquet-like expectation. Third, we extend the concept of uniform integrability for Choquet-like expectation. These results are useful for the solution of various problems in machine learning and made it possible to derive new efficient algorithms in any monotone system. Corresponding results are valid for capacities, the usefulness of which has been demonstrated by the rapidly expanding literature on generalized probability theory.
