Theory of Probability &Its Applications, Volume 67, Issue 1, Page 89-104, May 2022.
Uniform integrability is an interesting concept in probability theory and functional analysis since it plays an important role in establishing laws of large numbers. In the literature, there are several versions of uniform integrability. Some are defined with the help of matrix summability methods, such as the Cesàro matrix, or more general methods. In this paper, we introduce a new version of uniform integrability via power series summability methods. We investigate the relationships of this new concept with some previous concepts and give $L_1$- and $L_2$-convergence results for the laws of large numbers.

中文翻译：

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通过幂级数可和方法的新版本统一可积性

概率论及其应用，第 67 卷，第 1 期，第 89-104 页，2022 年 5 月。
一致可积性是概率论和泛函分析中的一个有趣概念，因为它在建立大数定律方面发挥着重要作用。在文献中，有几种统一可积性的说法。有些是在矩阵求和性方法的帮助下定义的，例如 Cesàro 矩阵，或更通用的方法。在本文中，我们通过幂级数可和方法介绍了一种新版本的统一可积性。我们研究了这个新概念与一些先前概念的关系，并给出了大数定律的 $L_1$- 和 $L_2$- 收敛结果。