Furstenberg entropy values for nonsingular actions of groups without property (T)
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Abstract:
Let $G$ be a discrete countable infinite group that does not have Kazhdan’s property (T) and let $\kappa$ be a generating probability measure on $G$. Then for each $t>0$, there is a type $III_1$ ergodic free nonsingular $G$-action whose $\kappa$-entropy (or the Furstenberg entropy) is $t$.References
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Additional Information
- Alexandre I. Danilenko
- Affiliation: Institute for Low Temperature Physics & Engineering of National Academy of Sciences of Ukraine, 47 Lenin Avenue, Kharkov, 61164, Ukraine
- MR Author ID: 265198
- Email: alexandre.danilenko@gmail.com, alexandre.danilenko@gmail.com
- Received by editor(s): December 16, 2015
- Received by editor(s) in revised form: May 4, 2016
- Published electronically: September 15, 2016
- Communicated by: Nimish Shah
- © Copyright 2016 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 145 (2017), 1153-1161
- MSC (2010): Primary 37A40; Secondary 37A20, 37A35
- DOI: https://doi.org/10.1090/proc/13278
- MathSciNet review: 3589315