The ergodic theorem for topological cocycles
In Ergodic Theory Dyn. Syst. 11, 19-39 (1991; Zbl 0723.60008), \textit{D. Boivin} and \textit{Y. Derriennic} published a definitive cocycle ergodic theorem generalizing the Birkhoff individual ergodic theorem in the context of a measurable action of the integer lattice \(\mathbb{Z}^m\) or the vector space \(\mathbb{R}^m\). The purpose of this paper is to show that for continuous cocycles an ergodic theorem of the same type can be proved by a more elementary approach using the original Birkhoff individual ergodic theorem and the Poincaré recurrence theorem with an application of the Ascoli lemma.
scientific article; zbMATH DE number 1309618