Amenable group
In mathematics, an amenable group is a locally compact topological group G carrying a kind of averaging operation on bounded functions that is invariant under translation by group elements. The original definition, in terms of a finitely additive measure (or mean) on subsets of G, was introduced by John von Neumann in 1929 under the German name "messbar" ("measurable" in English, although nowadays German mathematicians use the term "Mittelbare Gruppe") in response to the Banach–Tarski paradox.