向量值函数的Henstock-Stieltjes积分  

The Henstock-Stieltjes Integral of Vector-valued Functions

作　　者：王拉省[1] 薛红[1] 成涛[1] 

机构地区：[1]西安工程大学理学院,西安710048

出　　处：《工程数学学报》2007年第4期719-724,共6页Chinese Journal of Engineering Mathematics

基　　金：陕西省教育厅基金(05JK207);西安工程大学(2006XG32)

摘　　要：本文引入闭区间上实值函数关于向量值函数的Henstock-Stieltjes积分,研究了Henstock- Stieltjes积分的性质,给出了Henstock-Stieltjes积分可积的充要条件,并得到了Henstock- Stieltjes积分的收敛定理,最后证明了向量值函数在闭区间上关于实值右连续函数是Pettis可积,那么必为Henstock-Stieltjes可积。In this paper, we introduce and investigate the Henstock-Stieltjes integral for Banach-valued function with respect to a real valued function defined on closed intervals of the real line. The basic properties of the Henstock-Stieltjes integral are discussed. Some sufficent and necessary conditions for Henstock-Stieltjes integrable are given, and a convergence theorem is obtained. Finally, it is proved that a Pettis integrable function with respect to right continuous functions from a closed interval to a Banach space is Henstock-Stieltjes integrable.

关 键 词：Banach值函数 HENSTOCK-STIELTJES积分 收敛定理 PETTIS积分 

分 类 号：O177[理学—数学]