English

Generic properties of extensions

Dynamical Systems 2019-10-09 v6

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.

Keywords

Cite

@article{arxiv.1704.03709,
  title  = {Generic properties of extensions},
  author = {Mike Schnurr},
  journal= {arXiv preprint arXiv:1704.03709},
  year   = {2019}
}

Comments

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 fixed

R2 v1 2026-06-22T19:15:32.052Z