Problems of Absolute Continuity on Vector-Valued Functions

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.