可交换的随机变量和对称分布函数

The Commutative Random Variable and Symmetric Distribution Function

给出了可交换随机变量、对称分布函数和对称分布律的定义，讨论了它们之间的关系和性质，证明了对称分布律支撑在对称集上．

In this paper,we extend the interchangeable concept of finite random variable to sequence of random variable,and establish one to one correspondence of the interchangeable sequence of random variable,the symmetric and consistent distribution function family and the symmetric distribution law of enumerable infinite dimension space. We also prove that the symmetric distribution law μof infinite dimension space (R∞,)only depends on its value of cyliuder set class.