On normal numbers and self-similar measures

Amir Algom, Simon Baker, Pablo Shmerkin

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Let {f i(x)=s i⋅x+t i} be a self-similar IFS on R and let β>1 be a Pisot number. We prove that if [Formula presented] for some i then for every C 1 diffeomorphism g and every non-atomic self-similar measure μ, the measure gμ is supported on numbers that are normal in base β.

Original languageEnglish
Article number108276
Number of pages17
JournalAdvances in Mathematics
Early online date22 Feb 2022
Publication statusPublished - 16 Apr 2022


  • Normal numbers
  • Self-similar measures

ASJC Scopus subject areas

  • Mathematics(all)


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