On the convergence of bilateral ergodic averages
Volume 164 / 2021
Colloquium Mathematicum 164 (2021), 327-339
MSC: Primary 37A05.
DOI: 10.4064/cm7985-3-2020
Published online: 13 November 2020
Abstract
We study the almost sure convergence of bilateral ergodic averages for not necessarily integrable functions and relate it to the convergence of forward and backward averages, hence complementing results of Woś and the second named author. In the case of convergence, using results of Furstenberg on double recurrence, we prove oscillations of the bilateral ergodic averages around the limit.
