Amenability, Kazhdan's property <i>T</i>, strong ergodicity and invariant means for ergodic group-actions

Abstract

Abstract This paper discusses the relations between the following properties o finite measure preserving ergodic actions of a countable group G : strong ergodicity (i.e. the non-existence of almost invariant sets), uniqueness of G -invariant means on the measure space carrying the group action, and certain cohomological properties. Using these properties one can characterize all actions of amenable groups and of groups with Kazhdan's property T . For groups which fall in between these two definations these notions lead to some interesting examples.