English

Some factors of nonsingular Bernoulli shifts

Dynamical Systems 2021-08-06 v4 Probability

Abstract

We give elementary constructions of factors of nonsingular Bernoulli shifts. In particular, we show that all nonsingular Bernoulli shifts on a finite number 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-III:1 Bernoulli shifts of every possible ergodic index, answering a question of Danilenko and Lemanczyk (Ergodic Theory Dynam. Systems, 39(12):3292-3321, 2019).

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Cite

@article{arxiv.2010.04636,
  title  = {Some factors of nonsingular Bernoulli shifts},
  author = {Zemer Kosloff and Terry Soo},
  journal= {arXiv preprint arXiv:2010.04636},
  year   = {2021}
}

Comments

Published online at https://doi.org/10.4064/sm201013-7-4 in Studia Mathematica by the Institute of Mathematics, Polish Academy of Sciences