On winning sets and non-normal numbers

Details On winning sets and non-normal numbers On winning sets and non-normal numbers

2010-10-12

arxiv.org/abs/1010.2540v2

Mathematics

Number Theory

9 pages

Scientific paper

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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