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The Radon-Nikodym Property and Dentable Sets in Banach Spaces
W. J. Davis and R. R. Phelps
Proceedings of the American Mathematical Society
Vol. 45, No. 1 (Jul., 1974), pp. 119-122
Published by: American Mathematical Society
Stable URL: http://www.jstor.org/stable/2040618
Page Count: 4
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In order to prove a Radon-Nikodym theorem for the Bochner integral, Rieffel  introduced the class of "dentable" subsets of Banach spaces. Maynard  later introduced the strictly larger class of "s-dentable" sets, and extended Rieffel's result to show that a Banach space has the Radon-Nikodym property if and only if every bounded nonempty subset of E is s-dentable. He left open, however, the question as to whether, in a space with the Radon-Nikodym property, every bounded nonempty set is dentable. In the present note we give an elementary construction which shows this question has an affirmative answer.
Proceedings of the American Mathematical Society © 1974 American Mathematical Society