A characterization of the Radon-Nikodym property

2013/03/07 by Robert Deville, Deville, Robert, Óscar Madiedo +1
Mathematics · #46B20 #46B22 #91A05 #FOS: Mathematics #Functional Analysis (math.FA) #math.FA #msc:46B20 #msc:46B22 #msc:91A05

paper · pdf · doi:10.48550/arxiv.1303.1721

10 pages, 2 figures

arxiv created 2013/03/07 · arxiv updated 2013/03/08

Abstract

It is well known that every bounded below and non increasing sequence in the real line converges. We give a version of this result valid in Banach spaces with the Radon-Nikodym property, thus extending a former result of A. Procházka.

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