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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
DOI: 10.2307/2040618
Stable URL: http://www.jstor.org/stable/2040618
Page Count: 4
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The Radon-Nikodym Property and Dentable Sets in Banach Spaces
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Abstract

In order to prove a Radon-Nikodym theorem for the Bochner integral, Rieffel [5] introduced the class of "dentable" subsets of Banach spaces. Maynard [3] 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.

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