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The Hausdorff dimension
of a set of normal numbers
Andrew Douglas Pollington |
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Vol. 95 (1981), No. 1, 193–204
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Abstract |
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Suppose that numbers 2,3,⋯ are partitioned into two disjoint classes R, S so that rational powers lie in the same class. In this paper we prove that the set of numbers ξ which are normal to every base from R and to no base from S has Hausdorff dimension 1. The existence of such numbers was first shown by W. M. Schmidt. |
Mathematical Subject Classification
Primary: 10K25, 10K25
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Milestones
Received: 30 November 1979
Revised: 14 May 1980
Published: 1 July 1981
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Authors |
| Andrew Douglas Pollington | |
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