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Closed subgroups generated by generic measure automorphisms

Published online by Cambridge University Press:  08 January 2013

SŁAWOMIR SOLECKI
SŁAWOMIR SOLECKI*
Affiliation:
Department of Mathematics, 1409 W. Green St., University of Illinois, Urbana, IL 61801, USA (email: ssolecki@math.uiuc.edu)
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Abstract

We prove that for a generic measure-preserving transformation $T$, the closed group generated by $T$ is a continuous homomorphic image of a closed linear subspace of $L_0(\lambda , {\mathbb R})$, where $\lambda $ is the Lebesgue measure, and that the closed group generated by $T$contains an increasing sequence of finite-dimensional tori whose union is dense.

Type
Research Article
Information
Ergodic Theory and Dynamical Systems , Volume 34 , Issue 3 , June 2014 , pp. 1011 - 1017
Copyright
©2013 Cambridge University Press 

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