概率赋范线性空间的商空间

Quotient Space of Probabilistic Wormed Linear Space

本文提出了M—PN空间的概率商空间的概念,证明了完备的M—PN空间的概率商空间是完备的M—PN空间。此外还证明了在M—PN空间中,概率致紧、概率列紧、概率预紧、概率可分性对其概率商空间具有遗传性。

The notion of probabilistic quotient space of M—PN space is proposed in this paper. It is proved that probabilistic quotient space of complete M—PN space is complete M—PN space.