A variational Henstock integral characterization of the Radon-Nikodym property

Benedetto Bongiorno; Luisa Di Piazza; null Musiałl

A variational Henstock integral characterization of the Radon-Nikodym property

Benedetto Bongiorno, Luisa Di Piazza, Musiałl

Matematica e Informatica

Risultato della ricerca: Article

17 Citazioni (Scopus)

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 originale	English
pagine (da-a)	87-99
Numero di pagine	13
Rivista	Illinois Journal of Mathematics
Volume	53
Stato di pubblicazione	Published - 2009

All Science Journal Classification (ASJC) codes

Mathematics(all)

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Cita questo

Bongiorno, B., Di Piazza, L., & Musiałl (2009). A variational Henstock integral characterization of the Radon-Nikodym property. Illinois Journal of Mathematics, 53, 87-99.

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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.",

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author = "Benedetto Bongiorno and {Di Piazza}, Luisa and Musia{\l}l",

year = "2009",

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pages = "87--99",

journal = "Illinois Journal of Mathematics",

issn = "0019-2082",

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AU - Bongiorno, Benedetto

AU - Di Piazza, Luisa

AU - Musiałl, null

PY - 2009

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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

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 - Illinois Journal of Mathematics

JF - Illinois Journal of Mathematics

SN - 0019-2082

ER -