Abstract
It was shown by S. Kalikow and B.Weiss that, given a measure-preserving action of Zd on a probability space X and a nonnegative measurable function f on X, the probability that the sequence of ergodic averages 1/(2k + 1)d Σ gϵ[-k,...,k]d f(g - x) has at least n fluctuations across an interval (α β) can be bounded from above by c1cn 2 for some universal constants c1 ϵ R and c2 ϵ (0, 1), which depend only on d; α β. The purpose of this article is to generalize this result to measure-preserving actions of groups of polynomial growth. As the main tool we develop a generalization of the effective Vitali covering theorem to groups of polynomial growth.
Original language | English |
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Pages (from-to) | 255-273 |
Number of pages | 19 |
Journal | Studia Mathematica |
Volume | 240 |
Issue number | 3 |
DOIs | |
Publication status | Published - 2018 |
Keywords
- Fluctuations of ergodic averages
- Groups of polynomial growth