Hostname: page-component-78c5997874-dh8gc Total loading time: 0 Render date: 2024-11-11T07:34:17.489Z Has data issue: false hasContentIssue false
  • English
  • Français

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.
Get access

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

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

1.Bott, R.. Private communication.Google Scholar
2.Brown, G. and Moran, W.. Raikov systems and radicals in convolution measure algebras. J. London Math. Soc. (2) (1983), 531–542.CrossRefGoogle Scholar
3.Brown, G., Moran, W. and Pearce, C. E. M.. Riesz products and normal numbers. /. London Math. Soc. (2) (1985), 12–18.CrossRefGoogle Scholar
4.Brown, G., Moran, W. and Pearce, C. E. M.. Pearce. Riesz products, Hausdorff dimension and normal numbers. Math. Proc. Camb. Phil. Soc., 101 (1987), 529–540.CrossRefGoogle Scholar
5.Graham, C. C. and McGehee, O. C.. Essays in commutative harmonic analysis, Grundlehren der Mathematischen Wissenschaften 238 (Springer, New York, 1979).CrossRefGoogle Scholar
6.Pearce, C. E. M. and Keane, M. S.. On normal numbers. J. Aust. Math. Soc. (A) 32 (1982), 79–87.CrossRefGoogle Scholar
7.Pollington, A. D.. The Hausdorfi dimension of a set of normal numbers II. To appear, J. Aust. Math. Soc. (A).Google Scholar
8.Steinhaus, H.. Sur les distances des points des ensembles de mesure positive. Fund. Math., 1 (1920), 93–104.CrossRefGoogle Scholar
9.Talagrand, M.. Solution d'un problème de R. Haydon. Publ. Dép. Math. Lyon, 12 (1975), 43–46.Google Scholar
10.Woodall, D. R.. A theorem on cubes. Mathematika, 24 (1977), 60–62.CrossRefGoogle Scholar