m-相依样本三角组列的完全收敛性

讨论三角组列的完全收敛性。在较强的条件下，Hoerold Dehling讨论了独立同分布随机变量样本三角组列的收敛性问题，得到了一个较好的结果（定理A）。作者利用与Herold Dehling完全不同的方法，首先在较弱的情形下得到了独立同分布随机变量样本三角组列行和的完全收敛性（定理1），改进和加强了Herold Dehling的结果。同时考虑相依同分布样本的情形。在类似于定理1的较弱的假设下，利用不同的方法，得到m-相依同分布样布三角组列列和完全收敛性（定理2）。

Complete convergence of triangular arrays of m-dependent samples

Herold Dehling discussed the convergence property of triangular arrays of i. i. d. samples and obtained a result (Theorem A) under somewhat strong conditions. By using a different approach, the complete convergence of triangular arrays of i. i. d. samples under weak conditions(Theorem 1) is obtained. This result improves Dehling's one. At the same time, the case of m-dependent samples was discussed. By using defferent methods, the complete convergence of triangular arrays of m-dependent samples is obtained (Theorem 2) under assumption similar to the one in Theorem 1.