The Radon-Nikodým property and the Kreĭn-Milman property are equivalent for strongly regular sets

Schachermayer, Walter

doi:10.1090/S0002-9947-1987-0902791-8

The Radon-Nikodým property and the Kreĭn-Milman property are equivalent for strongly regular sets
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Trans. Amer. Math. Soc. 303 (1987), 673-687 Request permission

Abstract:

The result announced in the title is proved. As corollaries we obtain that RNP and KMP are equivalent for subsets of spaces with an unconditional basis and for $K$-convex Banach spaces. We also obtain a sharpening of a result of R. Huff and P. Morris: A dual space has the RNP iff all separable subspaces have the KMP.

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