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Transactions of the American Mathematical Society

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


Author: Walter Schachermayer
Journal: Trans. Amer. Math. Soc. 303 (1987), 673-687
MSC: Primary 46B22; Secondary 46G10
DOI: https://doi.org/10.1090/S0002-9947-1987-0902791-8
MathSciNet review: 902791
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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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DOI: https://doi.org/10.1090/S0002-9947-1987-0902791-8
Article copyright: © Copyright 1987 American Mathematical Society