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A CHARACTERIZATION OF THE WEAK RADON–NIKODÝM PROPERTY BY FINITELY ADDITIVE INTERVAL FUNCTIONS

Published online by Cambridge University Press:  07 September 2009

B. BONGIORNO
Affiliation:
Department of Mathematics, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy (email: [email protected])
L. DI PIAZZA
Affiliation:
Department of Mathematics, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy (email: [email protected])
K. MUSIAŁ*
Affiliation:
Institute of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland (email: [email protected])
*
For correspondence; e-mail: [email protected]
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Abstract

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A characterization of Banach spaces possessing the weak Radon–Nikodým property is given in terms of finitely additive interval functions. Due to that characterization several Banach space valued set functions that are only finitely additive can be represented as integrals.

Type
Research Article
Copyright
Copyright © Australian Mathematical Publishing Association Inc. 2009

Footnotes

The first and second authors were partially supported by MiUR, and all the authors were partially supported by grant N. 201 00932/0243.

References

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