一类基于扭曲概率测度的非可加积分的单调收敛定理
class of distorted probability measure’s non-additive integral’s monotone convergence theorem
本文主要研究了基于扭曲概率测度的Choquet积分的单调收敛定理，预期在一定条件下取得类似于经典概率论中（基于可加概率测度的）关于线性数学期望的单调收敛定理。论文由两部分组成：第一节为引言部分，介绍预备知识，；第二节是本文的主要内容。研究了一类基于扭曲概率的非可加积分的单调收敛性质（定理2.1）。为了证明这个结果，我们首先证明了四个命题，并最终使用列维（Levi）定理得到了上述结果。
his dissertation mainly discusses a class of distorted probability measure’s Choquet integral’s monotone convergence theorem, and excepted to achieve similar monotone convergence theorem under certain conditions. This thesis consists of two chapters: Chapter1 is a introduction, introduces some definitions; Chapter2 is the main content. We mainly study the distorted probability measure of non-additive integral’s monotone convergence property (Theorem 2.1). In order to prove this result, we first prove four propositions, and ultimately, we get the results by using Levi theorem.
李微微、张冬菊、候麟、于子晏、张靖芝
数学
集函数扭曲概率hoquet积分单调收敛性
Set functionistorted probabilityhoquet integralMonotone convergence property
李微微,张冬菊,候麟,于子晏,张靖芝.一类基于扭曲概率测度的非可加积分的单调收敛定理[EB/OL].(2010-04-07)[2025-08-11].http://www.paper.edu.cn/releasepaper/content/201004-246.点此复制
评论