向量值函数的绝对连续性问题

Problems of Absolute Continuity on Vector-Valued Functions

主要讨论定义于[0,1]区间,取值于Banach空间E的向量值函数的绝对连续性问题,易见强绝对连续必是绝对连续的,绝对连续必是弱绝对连续的,进一步说明了强绝对连续与(弱)绝对连续之间等价的充要条件是E为有限维的,也确实存在着无穷维空间,其中的绝对连续与弱绝对连续是相互等价的.

Absolutely continuous functions from Banach space have been discussed.And the strongly absolutely continuous is absolutely continuous,the absolutely continuous is weakly absolutely continuous.We also show some proterties of vector-valued functions that strongly absolutely continuous whenever it is（weakly） absolutely continuous if and only if E is finite dimension. This article also proves the absolutely continuous is equivalent to the weakly absolutely continuous in some infinite dimensional space.