An **amenable group** is a type of mathematical structure studied in the field of group theory, specifically in the study of topological groups and functional analysis. The concept of amenability is related to the ability of a group to have a certain type of "invariance" property under averaging processes. A group \( G \) is called **amenable** if it has a left-invariant mean.
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A discrete group is amenable when it admits a left-invariant finitely additive probability measure on all subsets of . Equivalently, it admits an invariant mean on the bounded real-valued functions on .