B值随机变量正则条件概率分布的存在性

Existence of B-valued random variable with regular conditional probability distribution

定义映射 φ :X→R∞ ={(ai) i≥ 1 |ai∈R},φ(x) =(ai) i≥1 ,其中x =∑∞i=1aiei.利用C[0 ,1 ]空间的万有性 ,即任一可分的Banach空间必等价于C[0 ,1 ]的一个闭子空间 ,证明了取值于完备可分度量空间的随机变量正则条件概率分布的存在性 ,并对该结论做了推广 :一是Banach空间是具有基的 ;

A mapping φ:X→R~∞={(ai)(i≥1)|ai∈R},φ(x)=(ai)(i≥1) and x=∑∞i=1aiei was defined, and then use the universal property of C[0,1] space, i.e., any separable Banack space is equivalent to a closed subspace of C[0, 1]. The results, which are existence of B-valued random variable with regular conditional probability distribution, obtained from this method extended into two cases: one was Banach spaces possessing basis, the other one was random variable itself being almost separable value.