Amenability and ergodic properties of topological groups: from Bogolyubov onwards

Abstract

The purpose of this expository article is to revisit the notions of amenability and ergodicity, and to point out that they appear for topological groups that are not necessarily locally compact in articles by Bogolyubov (1939), Fomin (1950), Dixmier (1950), and Rickert (1967).Comment: Terminology has been changed for reasons explained in Remark 3.15. Otherwise, minor corrections have been mad