关于容度的Fubini定理  

Fubini Theorems for Capacities

作　　者：王洪霞 WANG Hong-xia(Department of Statistics, Henan University of Economics and Law, Zhengzhou 450046 ,China;Analysis and Research Center on Education and Statistic Data of Henan Province,Zhengzhou 450046,China)

机构地区：[1]河南财经政法大学统计学院,河南郑州450046 [2]河南省教育统计数据分析与研究中心,河南郑州450046

出　　处：《模糊系统与数学》2018年第3期80-87,共8页Fuzzy Systems and Mathematics

基　　金：河南省高等学校重点科研项目(18A110011);校重大科研基金资助(855006)

摘　　要：Fubini定理是经典概率论和测度论中的一个基本概念,它在多元统计和随机过程中具有重要应用。近年来,在乘积代数和乘积σ-代数上关于容度的Fubini定理已分别被讨论,然而它们还只局限于对切面-共单调函数的特殊情形。本文主要基于一类更广义的既μ1-Choquet可积又μ2-Choquet可积函数研究关于凹(凸)容度的Fubini定理,进而推广了乘积σ-代数上关于容度的Fubini定理。Fubini Theorem is a basic concept in classical probability theory and measure theory,which has important applications in multivariate statistics and stochastic process.In recent years,the Fubini theorems on product algebras and productσ-algebras have been discussed respectively,but they are only limited to the special case of the slice-comonotonic functions.In this paper,we extend Fubini Theorems for concave（convex）capacities on productσ-algebras based on a larger class of functions,which are both μ1-Choquet integrable and μ_2-Choquet integrable.

关 键 词：FUBINI定理 凹容度 CHOQUET积分 

分 类 号：O211[理学—概率论与数理统计]