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Digit frequencies and Bernoulli convolutions

Research output: Contribution to journalArticle

Author(s)

Thomas Michael William Kempton

School/Research organisations

Abstract

It is well known that when β is a Pisot number, the corresponding Bernoulli convolution ν(β) has Hausdorff dimension less than 1, i.e. that there exists a set A(β) with (ν(β))(A(β))=1 and dim_H(A(β))<1. We show explicitly how to construct for each Pisot number β such a set A(β).
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Details

Original languageEnglish
Pages (from-to)832-842
JournalIndagationes Mathematicae
Volume25
Issue number4
DOIs
Publication statusPublished - 27 Jun 2014

    Research areas

  • Bernoulli convolutions, Beta expansions, Ergodic theory

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