泛积分的线性性  

On Linearity of the Pan-integrals

作　　者：李军[1] 季永静 张承坤 徐鹤萍 LI Jun;JI Yong-jing;ZHANG Cheng-kun;XU He-ping(School of Sciences,Communication University of China,Beijing 100024,China)

机构地区：[1]中国传媒大学理学院,北京100024

出　　处：《中国传媒大学学报（自然科学版）》2018年第1期9-14,共6页Journal of Communication University of China：Science and Technology

基　　金：国家自然科学基金(No.13371332)

摘　　要：本文讨论基于单调测度和泛运算的泛积分的线性性。利用单调测度的泛积分和对应于它的最优测度的泛积分之间的等价性和最优测度的特性我们证明了基于次泛可加单调测度的泛积分具有泛线性性和泛可加性,并且呈现了相应的泛积分的收敛性定理。In this note we discuss the linear of the pan-integral based on monotone measure and a pair of pan-operations.By means of the equivalence between the pan-integral with respect to monotone measure and the integral with respect to the optimal measure(corresponding the related monotone measure)and combining the characteristics of optimal measures we show that the pan-integrals based on pan-subadditive monotone measure possess the linearity and additivity.Following these results,the convergence theorems for pan-integrals are also presented.

关 键 词：单调测度 泛加法 泛乘法 泛积分 

分 类 号：O159[理学—数学]