几种绝对连续函数的等价性

EQUIVALENCE OF THE NOTIONS OF ABSOLUTE CONTINUITY

本文讨论了取值于Banach空间中函数的三种绝对连续相互等价性,得到强绝对 连续与绝对连续等价当且仅当空间是有限维的;绝对连续与弱绝对连续等价当且仅当空 间不含c0.

Absolutely continuous functions with values in Banach spaces have been dis-cussed. The main results of the paper are summarized as follows:The notions of weakly absolute continuity and absolute continuity of functions from [0,1] to a Banach space X are equivalent if and only if the space X containing no copy of c0 .