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.Comment: 29 pages; Lemma 7 strengthened and given a new proof; Former Lemma 6
  removed; Former Lemma 8 is now Lemma 6, with a slight reformulation; Typos
  fixe

Ageev

Einsiedler

Halmos

Katok

MIKE SCHNURR

Nadkarni

Robinson

Rokhlin

English

arXiv

Following the classical theory of Baire category results for sets of measure-preserving transformations, this work develops a theory for Baire category results for sets of measure-preserving extensions. First the case is considered where a measure space and a sub-algebra are fixed, and extensions are considered to be any measure-preserving transformations which leave this sub-algebra invariant. In the latter case, extensions of a fixed measure-preserving transformation are considered. In both cases, it is shown that the set of weakly mixing extensions form a dense, G-delta se

Schnurr, Michael

Qucosa - Publikationsserver der Universität Leipzig

Generic properties of extensions

HSSS - Hochschulschriftenserver der SLUB

Schnurr, M.

MPG.PuRe

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.</jats:p

Crossref

Ergodic Theory and Dynamical Systems

Qucosa

Generic properties of extensions

Abstract

Similar works

Full text

Available Versions

Qucosa - Publikationsserver der Universität Leipzig

HSSS - Hochschulschriftenserver der SLUB

MPG.PuRe

MPG.PuRe

Crossref

Qucosa