6533b7d8fe1ef96bd126a9cc
RESEARCH PRODUCT
A variational henstock integral characterization of the radon-nikodým property
B. BongiornoLuisa Di PiazzaK. Musiałlsubject
Settore MAT/05 - Analisi MatematicaHenstock integral Pettis integral variational measure Radon-Nikodym propertydescription
A characterization of Banach spaces possessing the Radon-Nikodym 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.
| year | journal | country | edition | language |
|---|---|---|---|---|
| 2009-01-01 |