罗曼诺夫斯基定理在Banach空间的推广

本文通过类似Stieltjes积分的处理,对在Banach空间取值的向量值函数f(t)和数值函数 g(t)定义integral from n=a to b(g(t)df(t) 、integral from n=a to b(f(t)dg(t)), 从而将其结果推广到Bochner可积的向量值函数。

A Generalization of Lomanrovski''''s Theorem to Banach Spaces

For a Lebesgue integrable function f (t) ,Lomanrovski has given certain conditions for thesingular integral dt to express the functional values at certain defined points. Bya treatment similar to stieltjes integral,this paper gives the definitions of dg (t) for a vector-valued function f(t) ranged in a Banach space and a numerical function g(t) , and generizes Lomanrovski's theorem to Bochner integrable vector-valued functions.