On Exposed Points of the Range of a Vector Measure. Ii

If a weakly compact convex set K in a real Banach space X is strongly exposed by a dense set of functionals in X', it is proved that the functionals which expose K form a residual set in A". If v. & -* X is a measure, it follows that the set of exposing functionals of its range is a residual Gs in A". This, in turn, is found to be equivalent to a theorem of B. Walsh on the residuality of functionals x' e X' for which x' ° v = v. If the set of exposed points of vi&) is weakly closed and vA is the restriction of v to any set A 6 S, it is further proved that every exposed point of the range of vA is of the form v{A n E), where E B & and d,E) is an exposed point of v(&).