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The Average Range Characterization of the Radon–Nikodym Property

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Abstract

A characterization of Banach spaces possessing the Radon—Nikodym property is given in terms of the average range of additive interval functions. We prove that a Banach space X has the RNP if and only if each X-valued additive interval function possessing absolutely continuous McShane (or Henstock) variational measure has nonempty average range almost everywhere on [0, 1].

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  1. Mathematics Department, Science Natural Faculty, University of Vlora, Vlora, Albania

    Sokol Bush Kaliaj

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  1. Sokol Bush Kaliaj
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Correspondence to Sokol Bush Kaliaj.

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Kaliaj, S.B. The Average Range Characterization of the Radon–Nikodym Property. Mediterr. J. Math. 11, 905–911 (2014). https://doi.org/10.1007/s00009-013-0352-3

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  • DOI: https://doi.org/10.1007/s00009-013-0352-3

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