可均群是数学上一个特别的局部紧拓扑群G，具备了一种为在G上的有界函数取平均的操作，而且G在函数上的群作用，不会改变所取得的平均。

在上的勒贝格测度，存在不可测的有界子集。豪斯多夫研究能否在上定义新的测度，使之可以对所有有界子集都是可测的。他要求新的测度保留勒贝格测度的等距变换不变性，就是移动及反射一个有界子集，不会改变其测度。不过，新测度无需有勒贝格测度的σ可加性（可数无限可加性），就是可数无限个不相交子集的测度总和，等于其并集的测度。他只要求新测度满足较弱的有限可加性，就是有限个不相交子集的测度总和，等于其并集的测度。

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 invariant measure (or mean) on subsets of G, was introduced by John von Neumann in 1929 under the German name "messbar" ("measurable" in English) in response to the Banach–Tarski paradox. In 1949 Mahlon M. Day introduced the English translation "amenable", apparently as a pun.