Under the framework of sub-linear expectation initiated by Peng, motivated by the concept of extended negative dependence, we establish a law of logarithm for arrays of row-wise extended negatively dependent random variables under weak conditions. Besides, the law of logarithm for independent and identically distributed arrays is derived more precisely and the sufficient and necessary conditions for the law of logarithm are obtained.

中文翻译：

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次线性期望下随机变量数组的对数定律

在彭提出的亚线性期望框架下，受扩展负相关概念的启发，我们建立了弱条件下逐行扩展负相关随机变量数组的对数定律。此外，更精确地推导出了独立同分布数组的对数定律，得到了对数定律的充要条件。