摘要
本文主要内容有三:其一,继承和发展了Menger的基本思想,建立起广义度量空间的理论体系,给概率度量空间、随机度量空间以及模糊度量空间等,提供了一个统一的理论框架。改进了文[4]、[6]的工作。其二,站在广义度量理论的角度,对若干概率度量标准之间的关系进行了讨论,部分地回答了文[8]中提出的问题。其三,讨论了广义度量空间的拓扑结构以及完备化问题,推广了文[2]的工作。
In this paper, firstly we advance generalized metric space system,with which probabilistic metric space,random metric spaces and fuzzy metric spaces are unified,and the results in [4]and [6]are improved.Then,the relations among some probabilistic metric scales are studied,and a problem in[8]is partly solved. Lastly, the topological structures of generalized metric spaces are researched;a completion theoriem in generalized metric space is proved, and the results in[2]are generalized.
出处
《工程数学学报》
CSCD
1996年第A12期37-44,共8页
Chinese Journal of Engineering Mathematics