Using an approach emerging from the theory of closable derivations on von Neumann algebras, we exhibit a class of groups satisfying the following property: given any groups , then any free, ergodic, measure-preserving action on a probability space gives rise to a von Neumann algebra with a unique group-measure space Cartan subalgebra. Pairing this result with Popa’s orbit equivalence superrigidity theorem we obtain new examples of -superrigid actions.
"Some unique group-measure space decomposition results." Duke Math. J. 162 (11) 1923 - 1966, 15 August 2013. https://doi.org/10.1215/00127094-2331230