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)

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.