Some factors of nonsingular Bernoulli shifts

Zemer Kosloff; Terry Soo

doi:10.4064/sm201013-7-4

Some factors of nonsingular Bernoulli shifts

Zemer Kosloff
, Terry Soo

Einstein Institute of Mathematics

Research output: Contribution to journal › Article › peer-review

2 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 language	English
Pages (from-to)	23-43
Number of pages	21
Journal	Studia Mathematica
Volume	262
Issue number	1
DOIs	https://doi.org/10.4064/sm201013-7-4
State	Published - 2022

Bibliographical note

Publisher Copyright:
© Instytut Matematyczny PAN, 2022.

Keywords

Bernoulli shifts
Krieger types
factors

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10.4064/sm201013-7-4

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N2 - 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].

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KW - Krieger types

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Some factors of nonsingular Bernoulli shifts

Abstract

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Keywords

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