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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.

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