English

Rational weak mixing in infinite measure spaces

Dynamical Systems 2021-08-16 v4 Probability

Abstract

Rational weak mixing is a measure theoretic version of Krickeberg's strong ratio mixing property for infinite measure preserving transformations. It requires "{\tt density}" ratio convergence for every pair of measurable sets in a dense hereditary ring. Rational weak mixing implies weak rational ergodicity and (spectral) weak mixing. It is enjoyed for example by Markov shifts with Orey's strong ratio limit property. The power, subsequence version of the property is generic.

Keywords

Cite

@article{arxiv.1105.3541,
  title  = {Rational weak mixing in infinite measure spaces},
  author = {Jon. Aaronson},
  journal= {arXiv preprint arXiv:1105.3541},
  year   = {2021}
}

Comments

Typos in the definitions of "rational weak mixing" and "weak rational ergodicity" (p.5) are corrected

R2 v1 2026-06-21T18:08:54.225Z