A characterization of Banach spaces possessing the Radon–Nikodým property is given in terms of finitely additive interval functions. We prove that a Banach space X has the RNP if and only if each X-valued finitely additive interval function possessing absolutely continuous variational measure is a variational Henstock integral of an X-valued function. Due to that characterization several X-valued set functions that are only finitely additive can be represented as integrals.
Publié le : 2009-05-15
Classification:
28B05,
26A39,
46G05,
46G10,
58C20
@article{1264170840,
author = {Bongiorno, B. and Di Piazza, L. and Musia\l , K.},
title = {A variational Henstock integral characterization of the Radon--Nikod\'ym property},
journal = {Illinois J. Math.},
volume = {53},
number = {1},
year = {2009},
pages = { 87-99},
language = {en},
url = {http://dml.mathdoc.fr/item/1264170840}
}
Bongiorno, B.; Di Piazza, L.; Musiał, K. A variational Henstock integral characterization of the Radon–Nikodým property. Illinois J. Math., Tome 53 (2009) no. 1, pp. 87-99. http://gdmltest.u-ga.fr/item/1264170840/