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RESEARCH PRODUCT

A Decomposition of Henstock-Kurzweil-Pettis Integrable Multifunctions

Luisa Di PiazzaKazimierz Musiał

subject

Discrete mathematicsPure mathematicsIntegrable systemRepresentation theoremSubadditivityBanach spaceDecomposition (computer science)Characterization (mathematics)MathematicsSeparable space

description

We proved in our earlier paper [9] that in case of separable Banach space-valued multifunctions each Henstock-Kurzweil-Pettis integrable multifunction can be represented as a sum of one of its Henstock-Kurzweil-Pettis integrable selectors and a Pettis integrable multifunction. Now, we prove that the same result can be achieved in case of an arbitrary Banach space. Applying the representation theorem we describe the multipliers of the Henstock-Kurzweil-Pettis integrable multifunctions. Then we use this description to obtain a characterization of the Henstock-Kurzweil-Pettis integrability in terms of subadditive operators.

yearjournalcountryeditionlanguage
2009-01-01
https://doi.org/10.1007/978-3-0346-0211-2_16