Some new results on integration for multifunction

Abstract

It has been proven in previous papers that each Henstock-Kurzweil-Pettis integrable multifunction with weakly compact values can be represented as a sum of one of its selections and a Pettis integrable multifunction. We prove here that if the initial multifunction is also Bochner measurable and has absolutely continuous variational measure of its integral, then it is a sum of a strongly measurable selection and of a variationally Henstock integrable multifunction that is also Birkhoff integrable.

15 pages

References in corpus (2)

• Gauge integrals and selections of weakly compact valued multifunctions
• Relations among Gauge and Pettis integrals for $cwk(X)$-valued multifunctions

Cited by in corpus (6)

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• Multifunctions determined by integrable functions
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• A vector Girsanov result and its applications to conditional measures via the Birkhoff integrability
• A Girsanov Result through Birkhoff Integral