Some factors of nonsingular Bernoulli shifts
Volume 262 / 2022
Studia Mathematica 262 (2022), 23-43
MSC: 37A40, 37A20, 37A35.
DOI: 10.4064/sm201013-7-4
Published online: 5 August 2021
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-$\mathrm {III}_{1}$ Bernoulli shifts of every possible ergodic index, answering a question of Danilenko and Lemańczyk [Ergodic Theory Dynam. Systems 39 (2019), 3292–3321].
