In this manuscript, we present a generalized deformed sum inspired by the nonadditive property of entropies such as those investigated by Tsallis and Shannon in the context of information theory. From this deformed sum, we define a generalization of the Vitali set and prove its nonmeasurability. Moreover, the standard sum is recovered as the deforming parameter tends to zero, and Vitali's theorem is retrieved. In particular, the present work is a generalization of the results derived in [2] for arbitrary functions satisfying general conditions, and not only nonextensive statistics.

中文翻译：

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关于一些任意变形和的广义维塔利集的注记

在这份手稿中，我们提出了一个广义变形和，其灵感来自熵的非加性特性，例如 Tsallis 和 Shannon 在信息论背景下所研究的那些。从这个变形的总和，我们定义了维塔利集的推广并证明了它的不可测性。此外，随着变形参数趋于零，标准和被恢复，维塔利定理被恢复。特别是，目前的工作是对满足一般条件的任意函数的 [2] 中得出的结果的概括，而不仅仅是非广泛的统计。