Use this tag for questions related to amenable groups, which are locally compact topological groups carrying a kind of averaging operation on bounded functions that is invariant under translation by group elements.
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 amenability property has a large number of equivalent formulations. In the field of analysis, the definition is in terms of linear functionals. An intuitive way to understand that version is that the support of the regular representation is the whole space of irreducible representations.
In discrete group theory, where G has the discrete topology, a simpler definition is used: A group is amenable if one can say what proportion of G any given subset takes up.
If a group has a Følner sequence, then the group is automatically amenable.
