Abstract
Sets of divergence points, i.e. numbers x (or tuples of numbers) for which the limiting frequency of a given string of N-adic digits of x fails to exist, have recently attracted huge interest in the literature. In this paper we consider sets of simultaneous divergence points, i.e. numbers x (or tuples of numbers) for which the limiting frequencies of all strings of N-adic digits of x fail to exist. We show that many natural sets of simultaneous divergence points are ( α, β)-wining sets in the sense of the Schmidt game. As an application we obtain lower bounds for the Hausdorff dimension of these sets.
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