LFP(ε)上两种拓扑的比较与LFP(S)的完备性
A Comparison of Two Topologies for LFP(ε) and the Completeness of LFP(S)
DOI: 10.12677/PM.2013.31013, PDF, HTML, 下载: 3,007  浏览: 11,907 
作者: 吴明智*：北京航空航天大学数学与系统科学学院；赵 媛*：河北金融学院基础部
关键词: 随机赋范模； (ε；λ)-拓扑；依概率收敛拓扑；Random Normed Module; (ε；λ)-Topology; Topology of Convergence in Probability
摘要: 首先，本文对上的-拓扑和依概率收敛拓扑作了一点初步的对比。接着，以为桥梁，利用其上两种拓扑的关系，运用随机赋范模理论中的一些结果给出Stricker引理的证明。最后，本文证明随机赋范模S生成的随机赋范模是完备的当且仅当S是完备的。
Abstract: First, we make a primary comparison of the -topology and the topology of convergence in probability for . Then, using the relation of the two kinds of topologies for , we give a proof of Stricker’s lemma based on a result in the theory of random normed modules. At last, we show that the random normed module is complete if and only if is complete.
文章引用：吴明智, 赵媛. LFP(ε) 上两种拓扑的比较与LFP(S) 的完备性[J]. 理论数学, 2013, 3(1): 81-86. http://dx.doi.org/10.12677/PM.2013.31013

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