摘要
本文系统地研究概率度量空间所特有的有界性与完全有界性.通过(ε,λ)-邻域,给出了有界性与完全有界性的刻画同时利用文献[4]中引入的概率度星空间上所特有的λ-拓扑,研究了P-性质与λ-性质之间的关系,以及λ-有界性、λ-完全有界性、λ-完备性、λ-紧性和λ-可分性之间的一系列关系,从而也得到了P-有界性、P-完全有界性、P-完备性、紧性以及可分性之间的一系列关系定理。
This paper is designed to study systematically the boundedness and complete boundedness of probabilisic metric spaces. The boundedness and comp1ete boundedness are characterized by (ε,λ) - neighborhood. Meanwhile, the relations between Pproperty and λ- property are revealed by the λ- topology introduced by [4]. In the same way, the relations between λ- boundedness, λ- complete boundedness, λ-completeness,λ-compactness and λ- separability are also obtained. Finally, a series ofrelation theorems about P - boundedness, P - complete boundedness, P - comp1eteness,P - compactness and P - separability are proved.
出处
《北方工业大学学报》
1995年第3期11-22,共12页
Journal of North China University of Technology
关键词
概率度量空间
λ-拓扑
有界性
完全有界性
probabilisic metric space
λ-topology
boundedness
complete boun dedness