A variational Henstock integral characterization of the Radon-Nikodym property

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Abstract

A characterization of Banach spacespossessing the Radon-Nikodym property is given in terms offinitely additive interval functions. We prove that a Banach spaceX has the RNP if and only if each X-valued finitely additiveinterval function possessing absolutely continuous variationalmeasure is a variational Henstock integral of an X-valuedfunction. Due to that characterization several X-valued setfunctions that are only finitely additive can be represented asintegrals.
Lingua originaleEnglish
pagine (da-a)87-99
Numero di pagine13
RivistaDefault journal
Volume53
Stato di pubblicazionePublished - 2009

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Radon-Nikodym Property
Stefan Banach
Absolutely Continuous Functions
If and only if
Interval
Term

All Science Journal Classification (ASJC) codes

  • Mathematics(all)

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title = "A variational Henstock integral characterization of the Radon-Nikodym property",
abstract = "A characterization of Banach spacespossessing the Radon-Nikodym property is given in terms offinitely additive interval functions. We prove that a Banach spaceX has the RNP if and only if each X-valued finitely additiveinterval function possessing absolutely continuous variationalmeasure is a variational Henstock integral of an X-valuedfunction. Due to that characterization several X-valued setfunctions that are only finitely additive can be represented asintegrals.",
keywords = "Henstock integral, Pettis integral, Radon-Nikodym property, variational measure",
author = "Benedetto Bongiorno and {Di Piazza}, Luisa and Musiałl",
year = "2009",
language = "English",
volume = "53",
pages = "87--99",
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TY - JOUR

T1 - A variational Henstock integral characterization of the Radon-Nikodym property

AU - Bongiorno, Benedetto

AU - Di Piazza, Luisa

AU - Musiałl, null

PY - 2009

Y1 - 2009

N2 - A characterization of Banach spacespossessing the Radon-Nikodym property is given in terms offinitely additive interval functions. We prove that a Banach spaceX has the RNP if and only if each X-valued finitely additiveinterval function possessing absolutely continuous variationalmeasure is a variational Henstock integral of an X-valuedfunction. Due to that characterization several X-valued setfunctions that are only finitely additive can be represented asintegrals.

AB - A characterization of Banach spacespossessing the Radon-Nikodym property is given in terms offinitely additive interval functions. We prove that a Banach spaceX has the RNP if and only if each X-valued finitely additiveinterval function possessing absolutely continuous variationalmeasure is a variational Henstock integral of an X-valuedfunction. Due to that characterization several X-valued setfunctions that are only finitely additive can be represented asintegrals.

KW - Henstock integral

KW - Pettis integral

KW - Radon-Nikodym property

KW - variational measure

UR - http://hdl.handle.net/10447/49043

M3 - Article

VL - 53

SP - 87

EP - 99

JO - Default journal

JF - Default journal

ER -