STRONGLY EXTREME-POINTS AND THE RADON-NIKODYM PROPERTY

We prove that if K is a bounded and convex subset of a Banach space X and x is a point in K, then x is a strongly extreme point of K if and only if x is a strongly extreme point of KBAR which is the weak* clos ure of K in X* . We also prove that a Banach space X has the Radon-Ni kodym property if and only if for any equivalent norm on X, the unit b all has a strongly extreme point.