NDLI: The Radon-Nikodym Property and Dentable Sets in Banach Spaces

Content Provider	Scilit
Author	Davis, W. J. Phelps, R. R.
Copyright Year	1974
Description	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 ``-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 is -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.
Related Links	http://www.ams.org/proc/1974-45-01/S0002-9939-1974-0344852-7/S0002-9939-1974-0344852-7.pdf
Ending Page	122
Page Count	4
Starting Page	119
ISSN	00029939
e-ISSN	10886826
DOI	10.2307/2040618
Journal	Proceedings of the American Mathematical Society
Issue Number	1
Volume Number	45
Language	English
Publisher	Duke University Press
Access Restriction	Open
Subject Keyword	Logic Radon Nikodym Dentable Sets Nikodym Property Banach Spaces
Content Type	Text
Resource Type	Article
Subject	Applied Mathematics

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The Radon-Nikodym Property and Dentable Sets in Banach Spaces