An extension of the Birkhoff integrability for multifunctions

Abstract

A comparison between a set-valued Gould type and simple Birkhoff integrals of $bf(X)$-valued multifunctions with respect to a non-negative set functionis given. Relationships among them and Mc Shane multivalued integrability is given under suitable assumptions.

arXiv comment24 pages

References in corpus (3)

• A note on comparison between Birkhoff and McShane-type integrals for multifunctions
• Order-type Henstock and McShane integrals in Banach lattice setting
• Comparison between some norm and order gauge integrals in Banach lattices

Cited by in corpus (8)

• Gauge integrals and selections of weakly compact valued multifunctions
• Some new results on integration for multifunction
• Properties of the Riemann-Lebesgue integrability in the non-additive case
• Multifunctions determined by integrable functions
• Kuelbs-Steadman spaces for Banach space-valued measures
• Atomicity related to non-additive integrability
• A vector Girsanov result and its applications to conditional measures via the Birkhoff integrability
• A Girsanov Result through Birkhoff Integral