| 关于随机最远点 |
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| 引用本文： | 赵世恩.关于随机最远点[J].应用泛函分析学报,2011,13(4):351-356. |
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| 作者姓名： | 赵世恩 |
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| 作者单位： | 北京航空航天大学数学与系统科学学院,北京100191;河北金融学院,保定071051 |
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| 摘 要： | 首先给出在随机赋范模中子集的随机最远点的概念．进一步，利用随机一致凸性和经典一致凸性之间的联系证明了下面的结果：令（E，｜｜·｜｜）为完备的随机一致凸的随机赋范模，S为E中几乎处处有界并在（ε, λ）一拓扑下的闭子集，则具有S中随机最远点的集合稠于E．
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| 关 键 词： | 随机赋范模 随机一致凸性 （ε λ）一拓扑 随机最远点 |
On Random Farthest Points |
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| ZHAO Shien.On Random Farthest Points[J].Acta Analysis Functionalis Applicata,2011,13(4):351-356. |
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| Authors: | ZHAO Shien |
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| Institution: | ZHAO Shien LMIB and School of Mathematics and Systems Science,Beihang University,Beijing 100191,China Hebei Finance University,Baoding 071051,China |
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| Abstract: | In this paper, we first present the notion of random farthest points of subsets in random normed modules. Then, we make use of the relation between random uniform convexity and classical uniform convexity to prove the following result： let （E, ｜｜·｜｜） be a complete random uniformly convex random normed module and S an almost surely bounded and closed subset of E under the （ε, λ）-topology, then the set of all points which have a random farthest point in S is dense in E. |
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| Keywords: | random normed module random uniform convexity (ε λ)-topology random farthest point |
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