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

  • B. BONGIORNO (a1), L. DI PIAZZA (a2) and K. MUSIAŁ (a3)
Abstract
Abstract

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.

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Copyright
Corresponding author
For correspondence; e-mail: musial@math.uni.wroc.pl
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The first and second authors were partially supported by MiUR, and all the authors were partially supported by grant N. 201 00932/0243.

Footnotes
References
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[1]Diestel J. and Uhl J. J., Vector Measures, Mathematical Surveys, 15 (American Mathematical Society, Providence, RI, 1977).
[2]Di Piazza L., ‘Variational measures in the theory of the integration in ℝm’, Czechoslovak Math. J. 51 (2001), 95110.
[3]Di Piazza L. and Musiał K., ‘Characterizations of Kurzweil–Henstock–Pettis integrable functions’, Studia Math. 176 (2006), 159176.
[4]Musiał K., ‘A characterization of the weak Radon–Nikodym property in terms of the Lebesgue measure’, in: Proceedings of the Conference Topology and Measure III, Part 1, 2 (Vitte/Hiddensee, 1980) (Wissensch. Beitr., Ernst-Moritz-Arndt Univ., Greifswald, 1982), pp. 163168.
[5]Musiał K., ‘Topics in the theory of Pettis integration’, Rend. Instit. Mat. Univ. Trieste 23 (1991), 177262.
[6]Musiał K., ‘Pettis integral’, in: Handbook of Measure Theory I (ed. E. Pap) (Elsevier, Amsterdam, 2002), pp. 531586.
[7]Pfeffer W. F., ‘The Lebesgue and Denjoy–Perron integrals from a descriptive point of view’, Ric. Mat. 48 (1999), 211223.
[8]Talagrand M., ‘Pettis integral and measure theory’, Mem. Amer. Math. Soc. 51(307) (1984).
[9]Thomson B. S., ‘Derivatives of interval functions’, Mem. Amer. Math. Soc. 452 (1991).
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Bulletin of the Australian Mathematical Society
  • ISSN: 0004-9727
  • EISSN: 1755-1633
  • URL: /core/journals/bulletin-of-the-australian-mathematical-society
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