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

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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.
Original languageEnglish
Number of pages17
JournalMathematical Proceedings of the Cambridge Philosophical Society
VolumeFirstView Article
Early online date7 Aug 2015
DOIs
Publication statusPublished - 2015

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