关于容度的Fubini定理

Fubini Theorems for Capacities

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.