A multivalued version of the Radon-Nikodym theorem, via the single-valued Gould integral
Domenico Candeloro, Anca Croitoru, Alina Gavrilut, Anna Rita, Sambucini
TL;DR
This paper extends the Radon-Nikodym theorem to multivalued measures using the Gould integral, providing new integrability results and a relative Radon-Nikodym theorem for multisubmeasures.
Contribution
It introduces a multivalued Radon-Nikodym theorem via the Gould integral, expanding the theory to M-spaces and multisubmeasures.
Findings
New integrability results for Gould integral on finite measure spaces
A Radon-Nikodym theorem for multisubmeasures with Gould integral
Extension of Radon-Nikodym theory to multivalued measures
Abstract
Some topics concerning the Gould integral are presented here: new results of integrability on finite measure spaces with values in an M-space are given, together with a Radon-Nikodym theorem relative to a Gould-type integral of real functions with respect to a multisubmeasure.
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Taxonomy
TopicsAdvanced Banach Space Theory · advanced mathematical theories · Stochastic processes and financial applications