Distribution of frequencies of digits via multifractal analysis

L Barreira, B Saussol, Jörg Schmeling

Research output: Contribution to journalArticlepeer-review

44 Citations (SciVal)


We study the Hausdorff dimension of a large class of sets in the real line defined in terms of the distribution of frequencies of digits for the representation in some integer base. In particular, our results unify and extend classical work of Borel, Besicovitch, Eggleston, and Billingsley in several directions. Our methods are based on recent results concerning the multifractal analysis of dynamical systems and often allow us to obtain explicit expressions for the Hausdorff dimension. This work is still another illustration of the role that the theory of dynamical systems can play in number theory.
Original languageEnglish
Pages (from-to)410-438
JournalJournal of Number Theory
Issue number2
Publication statusPublished - 2002

Subject classification (UKÄ)

  • Mathematics


  • multifractal analysis
  • frequencies of digits
  • Hausdorff dimension


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