概率度量空间的拓扑结构

TOPOLOGICAL STRUCTURE IN PROBABILISTIC METRIC SPACES

本文讨论了概率度量空间的拓扑结构,举例说明了在一般的概率度量空间上不一定建立按概率度量收敛的拓扑结构。提出了概率度量空间以集族U={U_p(ε,λ):P∈E,ε>0,λ>0}为邻域基的充分必要条件。

Topological structure in PM—spaces is disscussed in this paper. In general, It is impossible that an PM—space introduces a topological structure of PM—convergence. We give a necesary and sufficient condition for the family U= {U_P(ε, λ), P∈E, ε, λ>0} of sets to be a base for the neighborhoods in PM—spaces.