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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 in [2, p. 1047]. Also, several examples witnessing natural limits of our positive results are presented.2010 Mathematics Subject Classification. 46B99,46A55,26A21.

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Abstract. Let X, Y be compact convex sets such that every extreme point of X and Y is a weak peak point and both ext X and ext Y are Lindelöf spaces. We prove that if there exists an isomorphism T : A c (X) → A c (Y ) with T · T −1 < 2, then ext X is homeomorphic to ext Y . This generalizes results of C.

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