Disjointness for measurably distal group actions and applications
arXiv:1708.01934 · doi:10.1017/etds.2022.19
Abstract
We generalize Berg's notion of quasi-disjointness to actions of countable groups and prove that every measurably distal system is quasi-disjoint from every measure preserving system. As a corollary we obtain easy to check necessary and sufficient conditions for two systems to be disjoint, provided one of them is measurably distal. We also obtain a Wiener--Wintner type theorem for countable amenable groups with distal weights and applications to weighted multiple ergodic averages and multiple recurrence.
28 pages. v2: Small modifications in Section 6 as it previously used an incorrect result from [MR19] that has since been corrected in [MR21] (arxiv.org/abs/1609.03631)