几种绝对连续函数的等价性  

EQUIVALENCE OF THE NOTIONS OF ABSOLUTE CONTINUITY

作　　者：薛小平[1] 李志斌[2] 

机构地区：[1]哈尔滨工业大学数学系,哈尔滨150001 [2]大连铁道学院文理分院,大连116028

出　　处：《系统科学与数学》2004年第4期546-552,共7页Journal of Systems Science and Mathematical Sciences

基　　金：哈尔滨工业大学校基金(HIT.2002.53)资助课题.

摘　　要：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 .

关 键 词：绝对连续函数 等价性 有限维 BANACH空间 取值 

分 类 号：O174[理学—数学] O171[理学—基础数学]