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November 2015 Generalizations of some probability inequalities and $L^{p}$ convergence of random variables for any monotone measure
Hamzeh Agahi, Adel Mohammadpour, Radko Mesiar
Braz. J. Probab. Stat. 29(4): 878-896 (November 2015). DOI: 10.1214/14-BJPS251

Abstract

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.

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Hamzeh Agahi. Adel Mohammadpour. Radko Mesiar. "Generalizations of some probability inequalities and $L^{p}$ convergence of random variables for any monotone measure." Braz. J. Probab. Stat. 29 (4) 878 - 896, November 2015. https://doi.org/10.1214/14-BJPS251

Information

Received: 1 July 2012; Accepted: 1 May 2014; Published: November 2015
First available in Project Euclid: 17 September 2015

zbMATH: 1328.60051
MathSciNet: MR3397398
Digital Object Identifier: 10.1214/14-BJPS251

Rights: Copyright © 2015 Brazilian Statistical Association

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Vol.29 • No. 4 • November 2015
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