| 向量值函数的绝对连续性问题 |
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| 引用本文： | 董立华. 向量值函数的绝对连续性问题[J]. 广西师范学院学报(自然科学版), 2011, 28(1): 16-19 |
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| 作者姓名： | 董立华 |
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| 作者单位： | 德州学院数学系,山东德州,253023 |
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| 基金项目： | 山东省教育科学规划重点课题 |
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| 摘 要： | 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.
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| 关 键 词： | 绝对连续 强绝对连续 弱绝对连续 无条件收敛 绝对收敛 |
Problems of Absolute Continuity on Vector-Valued Functions |
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| DONG Li-hua. Problems of Absolute Continuity on Vector-Valued Functions[J]. Journal of Guangxi Teachers Education University:Natural Science Edition, 2011, 28(1): 16-19 |
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| Authors: | DONG Li-hua |
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| Affiliation: | DONG Li-hua(Department of Mathematics,Dezhou University,Dezhou 253023,P.R.China) |
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| Abstract: | 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. |
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| Keywords: | absolutely continuous strongly absolutely continuous weakly absolutely continuous unconditionally convergent absolutely convergent |
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