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

School of Mathematics

Research output: Contribution to journal › Article (Academic Journal) › peer-review

2 Citations (Scopus)

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

Original language	English
Pages (from-to)	23-43
Number of pages	21
Journal	Studia Mathematica
Volume	262
DOIs	https://doi.org/10.4064/sm201013-7-4
Publication status	Published - 5 Aug 2021

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title = "Some factors of nonsingular Bernoulli shifts",

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 Lema{\'n}czyk [Ergodic Theory Dynam. Systems",

author = "Zemer Kosloff and Terry Soo",

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AU - Kosloff, Zemer

AU - Soo, Terry

PY - 2021/8/5

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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

AB - 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

U2 - 10.4064/sm201013-7-4

DO - 10.4064/sm201013-7-4

M3 - Article (Academic Journal)

SN - 1730-6337

VL - 262

SP - 23

EP - 43

JO - Studia Mathematica

JF - Studia Mathematica

ER -

Some factors of nonsingular Bernoulli shifts

Abstract

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