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arXiv · 2010.04636

Some factors of nonsingular Bernoulli shifts

Zemer Kosloff·Terry Soo
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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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Zemer Kosloff, Terry Soo. 2020-10-09. Some factors of nonsingular Bernoulli shifts. https://doi.org/10.4064/sm201013-7-4

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