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On winning sets and non-normal numbers

2010/10/12 by Bill Mance, Mance, Bill
Computer Science · Mathematics · #11A63 #11K16 #Analytic Number Theory Research #FOS: Mathematics #Mathematical Approximation and Integration #Number Theory (math.NT) #Numerical Methods and Algorithms

paper · pdf · doi:10.48550/arxiv.1010.2540

openalex publication_date 2010/10/12 · openalex created_date 2016/06/24 · openalex updated_date 2026/08/03

Abstract

In \citeSchmidtGames, 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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