We study the strong law of large number for the sum of α mixing random variable sequences, apply these results in the weighted kernel estimator of nonparametric regression function proposed by Priestley, M.B. and Chao, M.T. ( 1972), and obtain better results. 研究α-混合序列加权和的强大数律,并将这些结果应用于Priestley,M.B.和Chao,M.T.(1972)提出的非参数回归函数加权核估计,获得较理想结论。