An extension of the Birkhoff integrability for multifunctions
Domenico Candeloro, Anca Croitoru, Alina Gavrilut, Anna Rita Sambucini
TL;DR
This paper compares different types of Birkhoff integrals for set-valued functions and explores their relationships with Mc Shane multivalued integrability under certain conditions.
Contribution
It extends the theory of Birkhoff integrability for multifunctions by comparing Gould type and simple Birkhoff integrals and analyzing their connections with Mc Shane integrability.
Findings
Comparison between Gould type and simple Birkhoff integrals
Relationships established with Mc Shane multivalued integrability
Conditions under which these integrals are equivalent or related
Abstract
A comparison between a set-valued Gould type and simple Birkhoff integrals of -valued multifunctions with respect to a non-negative set functionis given. Relationships among them and Mc Shane multivalued integrability is given under suitable assumptions.
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