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Endomorphisms of measured equivalence relations, cocycles with values in non-locally compact groups and applications

Published online by Cambridge University Press:  01 June 1999

ALEXANDRE I. DANILENKO
ALEXANDRE I. DANILENKO
Affiliation:
Department of Mechanics and Mathematics, Kharkov State University, Nezalezhnost' Sq. 4, Kharkov, 310077, Ukraine (e-mail: danilenko@ilt.kharkov.ua)
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Abstract

Consider a class of Polish groups arising from the subclass of amenable locally compact ones via operations of countable projective limit and group extensions. We show that for each group from this class there exists a cocycle of an ergodic transformation with dense range in it. This is applied to extend and provide a short (orbital) proof for one of the main results from [ALV] on non-coalescence of some ergodic skew product extensions.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 19 , Issue 3 , June 1999 , pp. 571 - 590
Copyright
1999 Cambridge University Press

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