PN空间中概率等度连续算子和概率拟有界

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，刚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．

Probabilisticly equicontinuous operator and probabilisticly quasi-bounded in PN space

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.