This article is cited in 7 papers

Radon–Nikodým Theorems for Multimeasures in Non-Separable Spaces

B. Cascales^a, V. Kadets^b, J. Rodríguez<sup>a

a</sup> Universidad de Murcia, 30100 Espinardo (Murcia), Spain
^b Department of Mechanics and Mathematics, V. N. Karazin Kharkov National University, 4 Svobody sq., Kharkiv 61022, Ukraine

Abstract: We prove two Radon–Nikodým theorems for multimeasures using set-valued Pettis integrable derivatives. The first one works for dominated strong multimeasures taking convex compact values in a locally convex space. The second one works for strong multimeasures taking bounded convex closed values in a Banach space with the RNP (and for Bochner integral of the Radon–Nikodým derivative as well). The main advantage of our results is the absence of any separability assumptions.

Key words and phrases: multimeasure, Radon–Nikodým theorem.

MSC: 28B05, 28B20, 46G10

Received: 08.02.2012
Revised: 07.06.2012

Language: English

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