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An inequality, with applications to Cantor measures and normal numbers

Published online by Cambridge University Press:  26 February 2010

Gavin Brown ,
Michael S. Keane ,
William Moran  and
Charles E. M. Pearce
Gavin Brown
Affiliation:
School of Mathematics, University of New South Wales, Kensington, N.S.W. 2033, Australia.
Michael S. Keane
Affiliation:
Department of Mathematics and Informatics, Delft University of Technology, Delft, 2600 A.J., The Netherlands.
William Moran
Affiliation:
Department of Pure Mathematics, University of Adelaide, Adelaide, S.A. 5001, Australia.
Charles E. M. Pearce
Affiliation:
Department of Applied Mathematics, University of Adelaide, Adelaide, S.A. 5001, Australia.
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Extract

Suppose x1, x2Є[0,1] and α = log 3/ log 4. Then

The relation is readily seen to be satisfied with equality for both of X1, x2 equal to any of the values 0, ½, 1 so that the value of α is “best possible”.

Type
Research Article
Information
Mathematika , Volume 35 , Issue 1 , June 1988 , pp. 87 - 94
Copyright
Copyright © University College London 1988

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