Amenable transformation groups have Følner-like nets, semidirect products allow investigation of amenability, and inner amenability is introduced with a characterization.
Stokke, Approximate diagonals and Følner conditions for amenable g roup and semigroup algebras , Studia Math., 164(2)(2004), 139-159
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Amenability and Inner Amenability of Transformation Groups
Amenable transformation groups have Følner-like nets, semidirect products allow investigation of amenability, and inner amenability is introduced with a characterization.