CAJ | 학술논문

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, 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) 空间中的概率等度连续算子的收敛算子是连续算子.(3) 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.
본문시운용개솔도량적사상래토론개솔등도련속산자, 급출료공간중개솔의유계집화개솔등도련속산자적개념, 연구료개솔등도련속산자적특성.주요득출료삼개연구결론:(1)재일정조건하, 공간중적개솔등도련속산자장개솔의유계집영사성개솔의유계집.(2) 공간중적개솔등도련속산자적수렴산자시련속산자.(3) 공간중적강유계산자시개솔등도련속산자, 차강유계적선성산자시련속산자.
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 space, the second conclusion of this paper is that probabilistic equicontinuous operator converges to a continuous operator in 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 space.