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The Spectrum of Completely Positive Entropy Actions of Countable Amenable Groups

✍ Scribed by A.H. Dooley; V.Ya. Golodets

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 189 KB
Volume: 196
Category: Article
ISSN: 0022-1236
DOI: 10.1006/jfan.2002.3966

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✦ Synopsis

We prove that an ergodic free action of a countable discrete amenable group with completely positive entropy has a countable Lebesgue spectrum. Our approach is based on the Rudolph-Weiss result on the equality of conditional entropies for actions of countable amenable groups with the same orbits. Relative completely positive entropy actions are also considered. An application to the entropic properties of Gaussian actions of countable discrete abelian groups is given.

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