  We give a shorter proof of a theorem of G. Elek stating that two hyperfinite
measure-preserving actions of a countable group on standard probability spaces
are approximately conjugate if and only if they have the same invariant random
subgroup. We then use this theorem to study model theory of hyperfinite
measure-preserving actions of countable groups on probability spaces. This work
generalizes the model-theoretic study of automorphisms of probability spaces
conducted by I. Ben Yaacov, A. Berenstein, C. W. Henson and A. Usvyatsov.
