Hyperfinite actions on countable sets and probability measure spaces
  We introduce the notion of hyperfiniteness for permutation actions of countable groups on countable sets and give a geometric and analytic characterization, similar to the known characterizations for amenable actions. We also answer a question of van Douwen on actions of the free group on two generators on countable sets. 
Miklos Abert and Gabor Elek
math.GR math.FA