L-值随机变量

L-valued Random Variables

研究L-值随机变量(其中L是闭集格或分子生成格与格上拓扑学有关)。受到已有文献中研究L-拓扑空间的思想、方法和技巧的启发,定义FLc(Rn)={A∈LRn对每个余素元,α{x∈Rn A(x)≥α}是Rn中的非空紧集}上一个分明拓扑TFLc以及L-子集族上的三种度量。在此基础上定义几种L-值随机变量并讨论了它们的初步性质。

We have investigated L-valued random variables （L is a closed-set lattice or moleculely generated lattice relating to lattice theory and topology）. Receiving already has inspiration of thought, method and skill studying L-topological space in documents, we have defined a crisp topology TFε^L on Fε^L（R^n） = {A∈LR^n ｜ for each a in Copr（L）, {x ∈R^n ｜A（x） ≥α} is non-empty compact set of R^n } and several kinds of metric on L-subset groups, some properties have discussed of them. On this basis, we have defined several L-valued random variables and discussed preliminary nature of them.