无穷个独立的随机变量序列的存在性

Existence of An Infinitely Sequence of Independent Random Variables

由给出的n(n∈Z+,n≥2)个分布函数,首先在可测空间(Rn,Rn)上构造概率测度Pn,接着构造n个随机变量,使之在概率空间(Rn,Rn,Pn)上是独立的,最后由科尔莫戈罗夫扩张定理得到在无穷维乘积空间(R)N,RN,μ(N={1,2,?})上无穷个独立的随机变量.

We construct probability measure with given n（n ∈ ＋,n ≥ 2） distribution functions, on the measurable space（Rn, n）, then construct n random variables on the probability space（Rn, n,Pn）, which are independent, and finally get an infinitely sequence of independent random variables on the infinite product space（R）N, N,μby the Kolmogorov＇s extension theorem.