On normal numbers and self-similar measures

Amir Algom, Simon Baker, Pablo Shmerkin

Research output: Contribution to journalArticlepeer-review


Let {fi(x)=si⋅x+ti} 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 C1 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
JournalAdvances in Mathematics
StatePublished - 16 Apr 2022
Externally publishedYes

Bibliographical note

Publisher Copyright:
© 2022 Elsevier Inc.


  • Normal numbers
  • Self-similar measures

ASJC Scopus subject areas

  • General Mathematics


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