子序列法应用条件的改进

Release of the applicative precondition of subsequence method

子序列法是在大数定理及其相关的收敛性证明中常使用的一种重要方法,主要应用在随机序列和的强收敛性定理证明中.本文将子序列法的应用条件从原有的独立序列扩展到某种意义上的正交序列,并给出了对一般随机变量序列所构成的级数的几乎处处收敛方法.

The method of subsequence is an important method which is usually used to prove convergence of the random sequence sum. In this paper, the preconditions of subsequence method are released from the independence sequence to the orthogonal sequence. And the method of almost sure convergence for a series constructed by general random variable sequences is given.