PN空间中概率等度连续算子和概率拟有界  

Probabilisticly equicontinuous operator and probabilisticly quasi-bounded in PN space

作　　者：徐旭华[1] 李亮[1] 张敏先[1] 

机构地区：[1]成都信息工程学院数学学院,四川成都610225

出　　处：《西南民族大学学报（自然科学版）》2009年第4期744-749,共6页Journal of Southwest Minzu University(Natural Science Edition)

摘　　要：本文是运用概率度量的思想来讨论概率等度连续算子,给出了PN空间中概率拟有界集和概率等度连续算子的概念,研究了概率等度连续算子的特性.主要得出了三个研究结论:(1)在一定条件下,PN空间中的概率等度连续算子将概率拟有界集映射成概率拟有界集.(2)PN空间中的概率等度连续算子的收敛算子是连续算子.(3)PN空间中的强有界算子是概率等度连续算子,次强有界的线性算子是连续算子.This paper uses the idea of probabilistic metric to analyse the probabilistic equicontinuous operator, gives the definition of probabilistic equicontinuous operator and probabilistic Quasi-bounded set, mainly studies the property of probabilistic equicontinuous operator. The first conclusion of this paper is that probabilistic equicontinuous operator is a probabilistic Quasi-bounded operator under some condition in PN space, the second conclusion of this paper is that probabilistic equicontinuous operator converges to a continuous operator in PN space, and the last conclusion of this paper is that the strong bounded operator is a probabilistic equicontinuous operator, a linear substrong bounded operator is a continuous operator in PN space.

关 键 词：PN空间 概率等度连续算子 概率拟有界集 τ-收敛 

分 类 号：O177.3[理学—数学]