A von Neumann algebra stf on a separable, complex Hilbert space %A has property A" if for every n x n array {f¡ } of elements in the predual there exists sequences {x,} , {>»■} in %? such that f¡ j(A) = (Ax¡, y ) for all A va. sá and 0 < i, j < n . We show that the von Neumann algebras with property AN are the von Neumann algebras with properly infinite commutant. We describe how these properties are transformed by the tensor product. We characterize the abelian von Neumann algebras with property An .