完备的W—空间

本文研究了随机半度量空间的a.s压缩性质与依概率度量压缩性质,所得结论推广了相关文献的相应结论,并结合几个有趣的注记说明:随机度量空间体系比概率度量空间体系与通常的度量空间体系更能揭示空间更为精细和深刻的性质——随机度量性质。

COMPLETE W-SPACES

The central purpose of this paper is to discuss a. s contraction mappings on a complete W-space in- troduced by J. B. Brown and probabilistic metric contraction mappings on the probabilistic metric space determined by the W-space. The main results of this paper,combined with several interesting remarks, show that random metric space system is different essentially from both probabilistic metric space sys- tem and ordinary metric space system. The distinction between them lies in the fact that random metric spece system possesses richer properties, i. e., random metric properties, than probabilistic metric space system and ordinary metric space system.