Some factors of nonsingular Bernoulli shifts

Zemer Kosloff, Terry Soo

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

We give elementary constructions of factors of nonsingular Bernoulli shifts. In particular, we show that all nonsingular Bernoulli shifts on a finite set of symbols which satisfy the Doeblin condition have a factor that is equivalent to an independent and identically distributed system. We also prove that there are type-III1 Bernoulli shifts of every possible ergodic index, answering a question of Danilenko and Lemańczyk [Ergodic Theory Dynam. Systems 39 (2019), 3292–3321].

Original languageAmerican English
Pages (from-to)23-43
Number of pages21
JournalStudia Mathematica
Volume262
Issue number1
DOIs
StatePublished - 2022

Bibliographical note

Publisher Copyright:
© Instytut Matematyczny PAN, 2022.

Keywords

  • Bernoulli shifts
  • Krieger types
  • factors

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