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Generic properties of extensions

Published online by Cambridge University Press:  13 March 2018

MIKE SCHNURR
MIKE SCHNURR*
Affiliation:
Max Planck Institute for Mathematics in the Sciences, Inselstr. 22, 04103 Leipzig, Germany email schnurr@mis.mpg.de
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Abstract

Motivated by the classical results by Halmos and Rokhlin on the genericity of weakly but not strongly mixing transformations and the Furstenberg tower construction, we show that weakly but not strongly mixing extensions on a fixed product space with both measures non-atomic are generic. In particular, a generic extension does not have an intermediate nilfactor.

Type
Original Article
Information
Ergodic Theory and Dynamical Systems , Volume 39 , Issue 11 , November 2019 , pp. 3144 - 3168
Copyright
© Cambridge University Press, 2018 

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