amenable

Amenable is an adjective describing a willingness to cooperate or be influenced, or the ability to be easily controlled or treated. In everyday use, it often means that someone is receptive to suggestions or authority: for example, the committee was amenable to changes. It can also describe something capable of being treated, managed, or influenced: the patient is amenable to therapy, or the problem is amenable to a straightforward solution. In more formal or legal language, it can imply submission to authority or jurisdiction, as in a matter that is amenable to arbitration. The term connotes cooperation and lack of resistance.

Etymology and usage notes: the word derives from Old French amenable, with senses tied to being amenable to amendment or influence, and entered English in the 17th century. It is not a synonym for hostility or obstinacy; rather, it emphasizes openness to suggestion, influence, or treatment.

In mathematics: amenable describes a class of groups that admit a left-invariant finitely additive probability measure on all of its subsets, or, equivalently, satisfy the Følner condition. Amenable groups include all finite groups and all abelian groups, and they arise in areas such as harmonic analysis and geometric group theory.

See also: tractable, compliant, cooperative, amenable to treatment, Følner condition, invariant mean.