﻿ L<sub>F</sub><sup style=" margin-left:-5px; margin-bottom:-2px;">P</sup>(ε) 上两种拓扑的比较与L<sub>F</sub><sup style=" margin-left:-5px; margin-bottom:-2px;">P</sup>(S) 的完备性

# 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)

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.

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