  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.
