Furstenberg entropy values for nonsingular actions of groups without property (T)

Furstenberg entropy values for nonsingular actions of groups without property (T)

Let G be a discrete countable infinite group that does not have Kazhdan’s property (T) and let κ be a generating probability measure on G. Then for each t > 0, there is a type III1 ergodic free nonsingular G-action whose κ-entropy (or the Furstenberg entropy) is t.

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Veröffentlicht in:Proceedings of the American Mathematical Society 2017-03, Vol.145 (3), p.1153-1161
1. Verfasser: DANILENKO, ALEXANDRE I.
Format: Artikel
Sprache:eng
Schlagworte:
B. ANALYSIS
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Zusammenfassung:Let G be a discrete countable infinite group that does not have Kazhdan’s property (T) and let κ be a generating probability measure on G. Then for each t > 0, there is a type III1 ergodic free nonsingular G-action whose κ-entropy (or the Furstenberg entropy) is t.
ISSN:0002-9939
1088-6826
DOI:10.1090/proc/13278