Ergodic subequivalence relations induced by a Bernoulli action

I. Chifan; A. Ioana

doi:10.1007/s00039-010-0058-7

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Ergodic subequivalence relations induced by a Bernoulli action

Journal article

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Ergodic subequivalence relations induced by a Bernoulli action

I. Chifan and A. Ioana

Geometric and Functional Analysis, Vol.20(1), pp.53-67

2010

DOI: 10.1007/s00039-010-0058-7

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Abstract

Let Γ be a countable group and denote by S the equivalence relation induced by the Bernoulli action Γ {right curved arrow} [0,1] Γ, where [0,1]Γ is endowed with the product Lebesgue measure. We prove that, for any subequivalence relation R of S, there exists a partition {Xi}i≥0 of [0,1]Γ into R-invariant measurable sets such that R{pipe}Xo is hyperfinite and R{pipe}Xi is strongly ergodic (hence ergodic and non-hyperfinite), for every i ≥ 1. © Birkhäuser / Springer Basel AG 2010.

Details

Title: Subtitle: Ergodic subequivalence relations induced by a Bernoulli action
Creators: I. Chifan - University of California, Los Angeles
A. Ioana - University of California, Los Angeles
Resource Type: Journal article
Publication Details: Geometric and Functional Analysis, Vol.20(1), pp.53-67
DOI: 10.1007/s00039-010-0058-7
ISSN: 1016-443X
Language: English
Date published: 2010
Academic Unit: Mathematics
Record Identifier: 9984230407402771

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