In this article, we employ the elementary inequalities arising from the sub-linearity of Choquet expectation to give a new proof for the generalized law of large numbers under Choquet expectations induced by 2-alternating capacities with mild assumptions. This generalizes the Linderberg–Feller methodology for linear probability theory to Choquet expectation framework and extends the law of large numbers under Choquet expectation from the strong independent and identically distributed (iid) assumptions to the convolutional independence combined with the strengthened first moment condition.

中文翻译：

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Choquet期望下的大数广义律的新证明

在本文中，我们利用了Choquet期望的次线性所产生的基本不等式，为由2个交替容量和温和假设引起的Choquet期望下的广义广义定律提供了新的证明。这将线性概率理论的Linderberg-Feller方法推广到Choquet期望框架，并将在Choquet期望下的大量定律从强大的独立且均匀分布（iid）假设扩展到卷积独立性并结合了增强的第一时刻条件。