Følner sequence

Summary

A Følner sequence in a countable group is a sequence of finite sets that become more and more invariant under translation, relative to their size. A countable group has a Følner sequence exactly when it satisfies the Følner condition, and this happens exactly when it is amenable. Følner sequences are the sets over which one averages in ergodic theorems for actions of amenable groups. In a locally compact group one uses compact sets of positive Haar measure instead of finite sets.