Abstract
It is shown that for Banach spaces the Radon-Nikodym property and the Bishop-Phelps property are equivalent. Using similar techniques, we prove that ifC is a bounded, closed and convex subset of a Banach space such that every nonempty subset ofC is dentable, then the strongly exposing functionals ofC form a denseG δ-subset of the dual.
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Bourgain, J. On dentability and the Bishop-Phelps property. Israel J. Math. 28, 265–271 (1977). https://doi.org/10.1007/BF02760634
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DOI: https://doi.org/10.1007/BF02760634