Structural Properties of Inner Amenable Groups

For infinite discrete groups, Effros introduced the notion of inner amenability which gives a new classification of discrete groups. The inner amenability is a considerably weaker condition than amenability, but closely related to the quite deep property . of groups. In this paper the author investigates the structures of inner amenable groups by theoretical set theory. A sequence of characterizations of inner amenable groups is given here by developing the well-known Folner's conditions for amenable locally compact groups.