Vol. 95, No. 1, 1981

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The Hausdorff dimension of a set of normal numbers

Andrew Douglas Pollington

Vol. 95 (1981), No. 1, 193–204
Abstract

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
Milestones
Received: 30 November 1979
Revised: 14 May 1980
Published: 1 July 1981
Authors
Andrew Douglas Pollington