Weak equivalence of stationary actions and the entropy realization   problem
  We introduce the notion of weak containment for stationary actions of a countable group and define a natural topology on the space of weak equivalence classes. We prove that Furstenberg entropy is an invariant of weak equivalence, and moreover that it descends to a continuous function on the space of weak equivalence classes. 
Peter Burton and Martino Lupini and Omer Tamuz
math.DS math.GR math.LO