Measurability of intersections of measurable multifunctions

We prove universal compact-measurability of the intersection of a compact-measurable Souslin family of closed-valued multifunctions. This generalizes previous result on intersections of measurable multifunctions. We introduce the unique maximal part of a multifunction which is defined on the quotient given by an equivalence relation. Measurability of this part of a multifunction is proven in a special case. We show how these results apply to the spectral theory of measurable families of closed linear operators