This paper provides sharp sufficient conditions for mean convergence of the maximal partial sums from triangular arrays of dependent random variables with general norming sequences. As an application, we use this result to give a positive answer to an open question in [Test 32(1):74–106, 2023] concerning mean convergence for the maximal partial sums under regularly varying moment conditions. The techniques developed in the present work also enable us to establish a result on mean convergence for sums of pairwise negatively dependent random variables, which gives an improvement of the main result of Sung [Appl Math Lett 26(1):18–24, 2013] and Ordóñez Cabrera and Volodin [J Math Anal Appl 305(2):644–658, 2005].

本文为具有一般范数序列的因随机变量三角阵列的最大部分和的均值收敛提供了尖锐的充分条件。作为一个应用，我们使用这个结果对 [Test 32(1):74–106, 2023] 中关于规则变化矩条件下最大部分和的平均收敛性的悬而未决的问题给出肯定的答案。本工作中开发的技术还使我们能够建立成对负相关随机变量之和的平均收敛结果，这改进了 Sung 的主要结果 [Appl Math Lett 26(1):18–24, 2013 ] 以及 Ordóñez Cabrera 和 Volodin [J Math Anal Appl 305(2):644–658, 2005]。