关键词： 几乎处处中心极限定理, NA序列, 子序列, Lipschitz 函数, 随机和

Abstract: The almost sure central limit theorem for the random sum of NA sequences is proved with the property of subsequence convergence. The almost sure central limit theorems is also proved under the weight conditions of 〖SX(〗1〖〗j〖SX)〗,〖SX(〗logλj〖〗j〖SX)〗 （λ>-1） and 〖SX(〗elog αj〖〗j〖SX)〗（α∈[0,1]）.

Key words: almost sure central limit theorem, NA sequence, subsequence, Lipschitz functions, random partial sums