Vol. 15, No. 4, 1965

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ISSN: 0030-8730
A set of nonnormal numbers

Michel Mendès France

Vol. 15 (1965), No. 4, 1165–1170
Abstract

Let P be the set of real polynomials and let E(P) be the the set of real numbers whose n-th binary digit from a certain point on is 0 or 1 according as [φ(n)] is even or odd for some φ P. We prove that no number in E(P) is normal in the binary system and that E(P) has Hausdorff dimension 0.

Mathematical Subject Classification
Primary: 10.33
Milestones
Received: 30 July 1964
Published: 1 December 1965
Authors
Michel Mendès France