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A VARIATIONAL McSHANE INTEGRAL CHARACTERISATION OF THE WEAK RADON–NIKODYM PROPERTY

Part of: Set functions, measures and integrals with values in abstract spaces

Published online by Cambridge University Press:  21 February 2012

SOKOL BUSH KALIAJ
SOKOL BUSH KALIAJ*
Affiliation:
Science Natural Faculty, Mathematics Department, University of Elbasan, Elbasan, Albania (email: sokol_bush@yahoo.co.uk)
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Abstract

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We present a characterisation of Banach spaces possessing the weak Radon–Nikodym property in terms of finitely additive interval functions whose McShane variational measures are absolutely continuous with respect to Lebesgue measure.

Keywords

weak Radon–Nikodym propertyBanach spacefinitely additive interval functionMcShane variational measure

MSC classification

Secondary: 28B05: Vector-valued set functions, measures and integrals
Type
Research Article
Information
Bulletin of the Australian Mathematical Society , Volume 85 , Issue 3 , June 2012 , pp. 456 - 462
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2012

References

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