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arxiv: 1010.2540 · v2 · pith:SIJUEH6Knew · submitted 2010-10-12 · 🧮 math.NT

On winning sets and non-normal numbers

classification 🧮 math.NT
keywords setsnon-normalnumberswinningbasecantorciteconsequence
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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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