标题:
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, 赵媛
关键字:
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
期刊名称:
《Pure Mathematics》, Vol.3 No.1, 2013-01-28
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。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.