The aim of this paper is to describe Henstock-Kurzweil-Pettis (HKP for short) integrable compact valued multifunctions. Such characterizations are known in case of functions. It is also known that each HKP-integrable compact valued multifunction can be represented as a sum of a Pettis integrable multifunction and of an HKP-integrable function. Invoking to that decomposition, we present a pure topological characterization of integrability. Having applied the above results, we obtain two convergence theorems, that generalize results known for HKP-integrable functions. We emphasize also the special role played in the theory by weakly sequentially complete Banach spaces and by spaces possessing the Schur property.

Di Piazza, L., Musial, K. (2013). Henstock-Kurzweil-Pettis integrability of compact valued multifunctions with values in an arbitrary Banach space. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 408(2), 452-464 [10.1016/j.jmaa.2013.05.073].

Henstock-Kurzweil-Pettis integrability of compact valued multifunctions with values in an arbitrary Banach space

DI PIAZZA, Luisa;
2013

Abstract

The aim of this paper is to describe Henstock-Kurzweil-Pettis (HKP for short) integrable compact valued multifunctions. Such characterizations are known in case of functions. It is also known that each HKP-integrable compact valued multifunction can be represented as a sum of a Pettis integrable multifunction and of an HKP-integrable function. Invoking to that decomposition, we present a pure topological characterization of integrability. Having applied the above results, we obtain two convergence theorems, that generalize results known for HKP-integrable functions. We emphasize also the special role played in the theory by weakly sequentially complete Banach spaces and by spaces possessing the Schur property.
Settore MAT/05 - Analisi Matematica
Di Piazza, L., Musial, K. (2013). Henstock-Kurzweil-Pettis integrability of compact valued multifunctions with values in an arbitrary Banach space. JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS, 408(2), 452-464 [10.1016/j.jmaa.2013.05.073].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/10447/82764
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