向量值函数的Henstock-Stieltjes积分

The Henstock-Stieltjes Integral of Vector-valued Functions

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.