Følner sequence

In mathematics, a Følner sequence for a group is a sequence of sets satisfying a particular condition. If a group has a Følner sequence with respect to its action on itself, the group is amenable. A more general notion of Følner nets can be defined analogously, and is suited for the study of uncountable groups. Følner sequences are named for Erling Følner.

Given a group ${\displaystyle G}$ that acts on a countable set ${\displaystyle X}$, a Følner sequence for the action is a sequence of finite subsets ${\displaystyle F_{1},F_{2},\dots }$ of ${\displaystyle X}$ which exhaust ${\displaystyle X}$ and which "don't move too much" when acted on by any group element. Precisely,

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