Pointwise ergodic theorems for higher levels of mixing
Volume 261 / 2021
Studia Mathematica 261 (2021), 329-344
MSC: Primary 37A25, 37A30; Secondary 37A05, 28D05.
DOI: 10.4064/sm200915-22-5
Published online: 9 August 2021
Abstract
We prove strengthenings of the Birkhoff Pointwise Ergodic Theorem for weakly mixing and strongly mixing measure preserving systems. We show that our pointwise theorem for weakly mixing systems is strictly stronger than the Wiener–Wintner Theorem. We also show that our pointwise theorems for weakly mixing and strongly mixing systems characterize those systems.
