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Transactions of the American Mathematical Society

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A geometrical characterization of Banach spaces with the Radon-Nikodym property


Author: Hugh B. Maynard
Journal: Trans. Amer. Math. Soc. 185 (1973), 493-500
MSC: Primary 46B05; Secondary 28A45, 46G10
DOI: https://doi.org/10.1090/S0002-9947-1973-0385521-0
MathSciNet review: 0385521
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Abstract: A characterization of Banach spaces having the Radon-Nikodym property is obtained in terms of a convexity requirement on all bounded subsets. In addition a Radon-Nikodym theorem, utilizing this convexity property, is given for the Bochner integral and it is easily shown that this theorem is equivalent to the Phillips-Metivier Radon-Nikodym theorem as well as all the standard Radon-Nikodym theorems for the Bochner integral.


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DOI: https://doi.org/10.1090/S0002-9947-1973-0385521-0
Keywords: Radon-Nikodym theorem, Radon-Nikodym property, Bochner integral, dentable, $ \sigma $-dentable
Article copyright: © Copyright 1973 American Mathematical Society