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)

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λ)-拓扑依概率收敛拓扑Random Normed Moduleλ)-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 (2013) LFP(ε) 上两种拓扑的比较与LFP(S) 的完备性。 理论数学, 3, 81-86. doi: 10.12677/PM.2013.31013

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