A Multivalued Version of the
Radon-Nikodym Theorem, via the Single-valued Gould Integral
A Multivalued Version of the Radon-Nikodym Theorem, via the Single-valued Gould Integral
Domenico Candeloro1, Anca Croitoru2, Alina Gavriluţ2, Anna Rita Sambucini1
1Dept. of Mathematics and Computer
University of Perugia,
1, Via Vanvitelli -- 06123, Perugia,
E-mail: firstname.lastname@example.org, email@example.com
2Faculty of Mathematics,
Al. I. Cuza University,
E-mail: firstname.lastname@example.org, email@example.com
In this paper we consider a Gould type integral of real functions with respect to a compact and convex valued not necessarily additive measure. In particular we will introduce the concept of integrable multimeasure and, thanks to this notion, we will establish an exact Radon-Nikodym theorem relative to a fuzzy multisubmeasure which is new also in the finite dimensional case. Some results concerning the Gould integral are also obtained.
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