摘要
R.AGordon在[1]中定义了从R1到Banach空间抽象函数的McShane积分,证明了当X不含C0时,如果f在[a,b]上McShanef可积,则在[a,b]上Petits 可积.在这篇文章中,我们定义了从Rn到Banaach空间抽象函数的Mcshane积分,证明了fMcShane可积,则f是Pattis可积.于是我们推广了[1]的结果.
R. A. Gordon[1] generalized the definition of the MeShane integral for real valued fonctions to the abstract functions from Rn to Banach spaces and pointed out that X contains no copy of c0,if a function f: [a,b]→X is McShane integrable on [a,b], then j is Petits integrable on I0. In this paper, we define the McShane integral for abstract functions borm Rn to Banach spaces. We prove that if a fortion f is McShane integrable on I0, then f is Petits integrable. So we extend the results of the [1].
出处
《数学研究》
CSCD
1998年第2期140-144,共5页
Journal of Mathematical Study