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Math. 22 (1978), 290-294. , On Banach spaces which contain £l(T) and types of measures on compact spaces, Israel J. Math. 28 (1977), 313-324. , On dual L1-spaces and injective bidual Banach spaces, Israel J. Math. 7 (1978), 142-152. , A non-reflexive Grothendieck space that does not contain £00 (to appear) . R. , Banach spaces whose duals are isomorphic to £, (f), J. Funct. Anal. 12 (1973), 177-187. (13) Lindenstrauss, J. , The ip-spaces, Israel J. Math. 7 (1969), 325-349. (14) Lindenstrauss, J.

E. ~(aeK) of the Krein = 1. We now have the following famous generalization Milman theorem Theorem 1. ([4J, [1'1J, [63J): (Choquet-BL;hop-de Leeuw) For any is a maximal probability meil,mre with resultant p E K there p. A nice proof of thi,; theorem hELJ been given by Anderues (8J. :::o,kEK} K 1:0 defined to be a simplex if a lattice cone. e. the [p EA(K)*lp(1) = 1 = lip))}. e. K is a simplex) . lattice cone in dimension 3 x Wehave([II], [1'1]' [63J): Theorem 2. (Choquet-Meyer) Each point of center of a unique maximal probability measure K is the bary- if and only if K is a simplex.

OLSEN dimensional simplex spaces. The non-separable case is still open, even for C(K)-spaces. Dualizing we have : Corollary. (Lazar-Lindenstrauss) plex. Let K be a metrizable sim- Then there exists a sequence of surjective affine projections Pn : lln+1 .... }~ 1 Let for l l= be the usual basis of Icon. e. a basis of the form isomorphism with where n II $11 = is an order I t is then easy to see that 1. is a permutation of Let (1,2, ... ,n}. an isometric order-isomorphism. In }~l= 1 in En so that 1

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