集值函数关于非可加集值测度的Choquet积分  

Choquet integral of set-valued functions with respect to multisubmeasures

作　　者：巩增泰[1] 魏朝琦[1] 

机构地区：[1]西北师范大学数学与统计学院,甘肃兰州730070

出　　处：《山东大学学报（理学版）》2015年第8期62-71,共10页Journal of Shandong University(Natural Science)

基　　金：国家自然科学基金资助项目(61262022;11461062)

摘　　要：按照集值积分的经典定义方法,不可避免地涉及集值函数和集值测度两方面的选择问题。本文利用集值函数关于非可加测度的实值Choquet积分,定义和讨论了集值函数关于非可加集值测度的Choquet积分,并刻画了其原函数性质。结果表明,弱零可加性、零可加性、凸零可加性、伪度量性质以及Darboux性质在其不定积分中均可遗传到其原函数中。It is inevitable for the problem how to deal with two aspects of selections for a set-valued function and a mul- tisubmeasure according to the classical definition method of the set-valued integral. The Choquet integral of a set-valued function with respect to a multisubmeasure is defined and discussed by using the real-valued Choquet integral of the set- valued function with respect to the non-additive measure, and some basic properties are characterized. It shows that a lot of characters could be well kept to their primitives such as the weakly null-additive, null-additive, converse null-addi- tive, the pseudometric property and the Darboux property, and so on.

关 键 词：集值函数 集值测度 CHOQUET积分 

分 类 号：O175.8[理学—数学]