Amenability and ergodic properties of topological groups: from   Bogolyubov onwards
  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). 
Rostislav Grigorchuk and Pierre de la Harpe
math.GR