On a co-induction question of Kechris

This note answers a question of Kechris: if H < G is a normal subgroup of a countable group G, H has property MD and G/H is amenable and residually finite, then G also has property MD. Under the same hypothesis we prove that for any action a of G, if b is a free action of G/H, and b_G is the induced action of G, then CInd^G_H (ɑ|H) × b_G weakly contains ɑ. Moreover, if H < G is any subgroup of a countable group G, and the action of G on G/H is amenable, then CInd^G_H (ɑ|H) weakly contains ɑ whenever ɑ is a Gaussian action.