有界闭凸值测度的集值积分  

The Set value integrals with respect to Set valued measure

作　　者：陈建斌[1] 王拉省[1] 

机构地区：[1]西安工程大学理学院,陕西西安710048

出　　处：《纯粹数学与应用数学》2007年第3期329-336,共8页Pure and Applied Mathematics

基　　金：陕西省教育厅专项基金(05JK207);西安工程大学校管项目(2006XG41)

摘　　要：引入实值函数关于有界闭凸值测度的集值积分,并讨论了集值积分的收敛定理,证明了当集值测度为有界闭凸集值的有界变差集值测度时,关于弱紧凸集值测度的积分性质对有界闭凸集值测度仍然保持.推广了实值函数关于弱紧凸值测度的积分.In this paper, the set valued Bratle integral of real valued functions with respect to bounded closed convex-valued measure is defined, and the properties of this integral on bounded closed convex-valued measure are discussed. The properties of integrals are shown to coincide in weakly compact set valued measure. Finally, we obtain the convergence theory of set valued integrals.

关 键 词：集值Bartle积分 有界变差集值测度 集值测度弱收敛 

分 类 号：O177.2[理学—数学]