On the Conjugacy of Measurable Partitions with Respect to the Normalizer of a Full Type Ergodic Group

Abstract: Let be a countable ergodic group of automorphisms of a measure space and be the normalizer of its full group. Problem: for a pair of measurable partitions and of the space, when does there exist an element such that ? For a wide class of measurable partitions, we give a solution to this problem in the case where is an approximately finite group with finite invariant measure. As a consequence, we obtain results concerning the conjugacy of the commutative subalgebras that correspond to and in the type factor constructed via the orbit partition of the group.