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arXiv · 1010.2540

On winning sets and non-normal numbers

Bill Mance
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Abstract

In \cite{SchmidtGames}, W. Schmidt proved that the set of non-normal numbers in base $b$ is a {\it winning set}. We generalize this result by proving that many sets of non-normal numbers with respect to the Cantor series expansion are winning sets. As an immediate consequence, these sets will be shown to have full Hausdorff dimension.

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Bill Mance. 2010-10-12. On winning sets and non-normal numbers. https://arxiv.org/abs/1010.2540

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