Conjecture: In general a mixing transformation is not two-fold mixing
type: Item
instance of: scholarly article
title: Conjecture: In general a mixing transformation is not two-fold mixing
zbMATH Open document ID: 0574.28012
published in: The Annals of Probability
publication date: 1985-01-01T00:00:00Z
review text: In this paper an attempt to solve an old problem whether a mixing transformation is two-fold mixing is made. A new topology in the space of all automorphisms of a Lebesgue space is introduced. In this topology the subspace of mixing automorphisms is a Baire space. Next, under the assumption of the validity of some conjecture, it is shown that the two- fold mixing automorphisms are of first category in the mixing ones. Hence, there exists a mixing automorphism which is not two-fold mixing. The above mentioned conjecture concerns the extent to which a mixing stationary process is determined by its two-dimensional distributions.
Mathematics Subject Classification ID: 28D05
Mathematics Subject Classification ID: 54E52
zbMATH DE Number: 3916634
zbMATH Keywords: mixing transformation
zbMATH Keywords: topology in the space of all automorphisms of a Lebesgue space
zbMATH Keywords: Baire space
zbMATH Keywords: the two-fold mixing automorphisms are of first category in the mixing ones
zbMATH Keywords: mixing stationary process
zbMATH Keywords: two- dimensional distributions
Wikidata QID: Q122904921
author: Steve Alpern
reviewed by: Janusz Woś
MaRDI profile type: Publication
full work available at URL: https://doi.org/10.1214/aop/1176993084
OpenAlex ID: W1983433226
DOI: 10.1214/AOP/1176993084
description: scientific article; zbMATH DE number 3916634