Abelian cocycles for nonsingular ergodic transformations and the genericity of type \(III_ 1\) transformations
type: Item
instance of: scholarly article
title: Abelian cocycles for nonsingular ergodic transformations and the genericity of type \(III_ 1\) transformations
zbMATH Open document ID: 0623.58010
DOI: 10.1007/BF01364339
author: J. R. Choksi
author: Jane Hawkins
author: V. S. Prasad
published in: Monatshefte für Mathematik
publication date: 1987-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/178325
review text: The authors prove that in the space of nonsingular transformations of a Lebesgue probability space the type \(III_ 1\) ergodic transformations form a dense \(G_{\delta}\) set with respect to the coarse topology. They also prove that for any locally compact second countable abelian group H, and any ergodic type III transformation T, it is generic in the space of H-valued cocycles for the integer action given by T that the skew product of T with the cocycle is orbit equivalent to T. Similar results are given for ergodic measure-preserving transformations as well.
Mathematics Subject Classification ID: 37A99
zbMATH DE Number: 4011471
zbMATH Keywords: nonsingular transformations
zbMATH Keywords: probability space
zbMATH Keywords: ergodic transformations
zbMATH Keywords: skew product
MaRDI profile type: Publication
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OpenAlex ID: W1987865773
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description: scientific article; zbMATH DE number 4011471