Følner condition

Summary

A group satisfies the Følner condition when it has finite subsets that are almost invariant under translation. Moving such a set by a given element changes only a small fraction of it. A sequence of such sets is a Følner sequence. By Følner's theorem, a discrete group satisfies the condition exactly when it is amenable. Følner sequences are the natural sets over which to take averages in ergodic theorems for group actions.