On winning sets and non-normal numbers
Number Theory
2010-11-03 v2
Abstract
In \cite{SchmidtGames}, W. Schmidt proved that the set of non-normal numbers in base 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.
Cite
@article{arxiv.1010.2540,
title = {On winning sets and non-normal numbers},
author = {Bill Mance},
journal= {arXiv preprint arXiv:1010.2540},
year = {2010}
}
Comments
9 pages