Lebesgue-Stieltjes形式的Choquet积分

Choquet Integral Defined by Lebesgue-Stieltjes Integral

首先利用Lebesgue-Stieltjes测度对Choquet积分作了推广,给出了实值可测函数的Lebesgue-Stieltjes形式的Choquet积分的定义,研究了其相应的性质;其次,本文在一定条件下研究了Lebesgue-Stieltjes形式的Choquet积分和Choquet积分的关系,得到了积分转化定理。

This paper first generalizes Choquet integral by making use of Lebesgue-Stieltjes measure, it gives the definition of Choquet integral defined byLebesgue-Stieltjes integral and rearches some properties of this new integral; then, it researches the relationship between Choquet integral defined by LebesgueStieltjes integral and Choquet integral, so integral conversion theorem is shown.