The isomorphism of measure-preserving transformations with isomorphic Cartesian powers is typical
type: Item
instance of: scholarly article
title: The isomorphism of measure-preserving transformations with isomorphic Cartesian powers is typical
zbMATH Open document ID: 0882.28014
DOI: 10.1007/BF02308696
author: Valery Ryzhikov
published in: Mathematical Notes
publication date: 1997-07-14T00:00:00Z
review text: The author tries to answer the following question: If \(S\) and \(T\) are measure-preserving transformations of a Lebesgue probability space \((X,\mu)\) such that \(\times_1^d S\) and \(\times_1^d T\) are metrically isomorphic, does imply this condition that \(T\) and \(S\) are isomorphic? He proves that if \(T\) is a \(\chi\)-mixing automorphism, \(0<\chi<1\), and an automorphism \(S\) satisfies the relation \[ \Phi(S\otimes\ldots\otimes S)\Phi^{-1}= T\otimes\ldots\otimes T \] where \(\Phi\) is the operator corresponding to a measure-preserving transformation of \(\times_1^d X\) with measure \(\times_1^d \mu\), then \(S\) and \(T\) are isomorphic.
Mathematics Subject Classification ID: 28D05
zbMATH DE Number: 1028549
zbMATH Keywords: measure-preserving transformation
reviewed by: Emilia Petrisor
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 1028549