Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. 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 left translation by group elements. The original definition, in terms of a finitely additive invariant measure on subsets of G, was introduced by John von Neumann in 1929 under the German name "messbar" in response to the Banach–Tarski paradox. In 1949 Mahlon M. Day introduced the English translation "amenable", apparently as a pun.

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