| 几种绝对连续函数的等价性 |
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| 引用本文： | 薛小平,李志斌. 几种绝对连续函数的等价性[J]. 系统科学与数学, 2004, 24(4): 546-552 |
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| 作者姓名： | 薛小平 李志斌 |
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| 作者单位： | 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 |
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| 基金项目： | 哈尔滨工业大学校基金(HIT.2002.53)资助课题. |
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| 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.
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| 关 键 词： | 绝对连续性 等价 不含coBanach空间 |
| 修稿时间： | 2001-11-21 |
EQUIVALENCE OF THE NOTIONS OF ABSOLUTE CONTINUITY |
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| Xiao Ping XUE,Zhi Bin LI. EQUIVALENCE OF THE NOTIONS OF ABSOLUTE CONTINUITY[J]. Journal of Systems Science and Mathematical Sciences, 2004, 24(4): 546-552 |
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| Authors: | Xiao Ping XUE Zhi Bin LI |
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| Affiliation: | (1)Department of Mathematics, Harbin Institute of Technology, harbin 150001;(2)Dalian Railway Institute, Dalian 116028 |
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| Abstract: | 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 . |
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| Keywords: | absolute continuity equivalence Banach space containing no copy c0. |
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