On the continuity of the support of bimodules over maximal abelian self-adjoint algebras

We relate the convergence of a net of maximal Abelian selfadjoint algebras (masas) to that of the net of their corresponding supports. This is achieved by using a family of capacities on the collection of subsets of X × Y (where the masas are realized as collections of operators of multiplication by essentially bounded functions on the measure spaces X and Y), which extends a capacity studied previously by Haydon and Shulman.