| Banach空间的弱Lebesgue性质与弱*Lebesgue性质 |
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| 引用本文： | 杨振华. Banach空间的弱Lebesgue性质与弱*Lebesgue性质[J]. 南京邮电大学学报(自然科学版), 2001, 21(3): 50-52 |
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| 作者姓名： | 杨振华 |
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| 作者单位： | 南京邮电学院应用数理系, |
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| 摘 要： | 讨论了取值于上Banach空间上的各种积分与弱 拓扑之间的关系。证明了对于具有可分共扼空间的Banach空间 ,在有界性条件下 ,映射的数量Riemann可积性与几乎处处弱连续性是等价的。引进了弱 Lebesgue性质的概念 ,证明了可分空间的共扼空间具有弱 Lebesgue性质。最后证明了 ,对于具有弱 Lebesgue性质的Banach空间 ,Riemann可积映射是Bochner可积的。
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| 关 键 词： | Banach空间 Riemann积分 弱Lebesgue性质 弱*Lebesgue性质 |
| 文章编号： | 1000-1972(2001)03-0050-03 |
| 修稿时间： | 2001-03-20 |
On the Weak and Weak* Lebesgue Property of Banach Space |
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| YANG Zhen-hua. On the Weak and Weak* Lebesgue Property of Banach Space[J]. JJournal of Nanjing University of Posts and Telecommunications, 2001, 21(3): 50-52 |
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| Authors: | YANG Zhen-hua |
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| Abstract: | The relationship between integrate over Banach space and weak and weak* topology is discussed.It is proved that over Banach space with separable dual,for bounded mapping,the weak continuity and scalarly Riemann integrability is equivalent.With the concept of Weak* Lebesgue Property defined,it is proved that the dual of separable space has Weak* Lebesgue Property.Finally,it is showed that for Banach space with Weak* Lebesgue Property,the Riemann integrable mapping is Bochner integrable. |
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| Keywords: | Banach space Riemann integral Weak lebesgue property Weak* lebesgue property |
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