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On the exact rate of convergence of frequencies of digits and local dimensions of multinomial measures

Published online by Cambridge University Press:  07 August 2015

L. OLSEN
L. OLSEN*
Affiliation:
Department of Mathematics, University of St. Andrews, St. Andrews, Fife KY16 9SS, Scotland. e-mail: [email protected]
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Abstract

We study the Hausdorff dimensions of certain sets of non-normal numbers defined in terms of the exact rate of convergence of digits in their N-adic expansions. As an application of our results we analyse the rate of convergence of local dimensions of multinomial measures.

Type
Research Article
Information
Mathematical Proceedings of the Cambridge Philosophical Society , Volume 159 , Issue 3 , November 2015 , pp. 387 - 403
Copyright
Copyright © Cambridge Philosophical Society 2015 

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References

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