Maximizing Bernoulli measures and dimension gaps for countable branched systems

S Baker, N Jurga

Research output: Contribution to journalArticlepeer-review


Kifer, Peres, and Weiss proved in [A dimension gap for continued fractionswith independent digits. Israel J. Math. 124 (2001), 61–76] that there exists c0 > 0,such that dim µ ≤ 1 − c0 for any probability measure µ, which makes the digits of thecontinued fraction expansion independent and identically distributed random variables. Inthis paper we prove that amongst this class of measures, there exists one whose dimensionis maximal. Our results also apply in the more general setting of countable branchedsystems
Original languageEnglish
Pages (from-to)1921-1939
Number of pages19
JournalErgodic Theory and Dynamical Systems
Issue number7
Early online date26 May 2020
Publication statusPublished - Jul 2021


  • Continued fractions
  • Bernoulli measures
  • Dimensions of measures


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