The Haagerup property for measure preserving standard equivalence relations

We define a notion of the Haagerup property for measure-preserving standard equivalence relations. Given such a relation R on X with finite invariant measure mu, we prove that R has the Haagerup property if and only if the associated finite von Neumann algebra L(R) (see J. Feldman and C. C. Moore. Ergodic equivalence relations, cohomology and von Neumann algebras II. Trans. Amer. Math. Soc. 234 (1977), 325-350) has relative property H in the sense of Popa with respect to its natural Cartan subalgebra L-infinity(X, mu). We also prove that if G is a countable group such that R = R-G has the Haagerup property and if R is ergodic, then G cannot have Kazhdan's property T.