任意随机变量序列的一类强极限定理

A Class of Strong Limit Theorems for the Sequence of Arbitrary Random Variables

对任意的实值随机变量序列｛ Ｘｎ ，ｎ ≥１｝ 以及函数列｛φｎ（ｘ） ，ｎ≥１｝ ，研究了随机序列｛ φｎ（ Ｘｎ），ｎ ≥１｝ 的强极限定理，所得的结果是经典的独立随机变量序列的极限定理的推广．

For sequence of arbitrary real valued random variables ｛ X n,n≥1 ｝ and sequence of functions ｛ φ n(x),n≥1 ｝,we studied the strong limit theorems of random sequence ｛φ n(X n),n≥1｝ .The theorems generalizes some classical limit theorems for the sequence of independent random variables.