If $E$ is a Banach space, any element $x^{ **}$ in its bidual $E^{ **}$ is an affine function on the dual unit ball $B_{ E^*}$ that might possess variety of descriptive properties with respect to the weak* topology. We prove several results showing that descriptive properties of $x^{ **}$ are quite often determined by the behaviour of $x^{ **}$ on the set of extreme points of $B_{ E^*}$, generalizing thus results of J. Saint Raymond and F. Jellett. We also prove several results on relation between Baire classes and intrinsic Baire classes of $L_1$-preduals which were introduced by S.A. Argyros, G. Godefroy and H.P. Rosenthal. Also, several examples witnessing natural limits of our positive results are presented.
Categories: math.FA