A Note on Generalized Vitali Sets with Respect to Some Arbitrary Deformed Sums

Abstract

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.