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Transactions of the American Mathematical Society

Published by the American Mathematical Society, the Transactions of the American Mathematical Society (TRAN) is devoted to research articles of the highest quality in all areas of pure and applied mathematics.

ISSN 1088-6850 (online) ISSN 0002-9947 (print)

The 2020 MCQ for Transactions of the American Mathematical Society is 1.43.

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The Radon-Nikodým property and the Kreĭn-Milman property are equivalent for strongly regular sets
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by Walter Schachermayer PDF
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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Additional Information
  • © Copyright 1987 American Mathematical Society
  • 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