Radon-Nikodym derivatives of finitely additive interval measures taking values in a Banach space with basis |
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| Authors: | Benedetto BONGIORNO Luisa DI PIAZZA Kazimierz MUSIAL |
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| Institution: | (1) Department of Mathematics, University of Palermo, Via Archirafi 34, 90123 Palermo, Italy;(2) Institut of Mathematics, Wrocław University, Pl. Grunwaldzki 2/4, 50-384 Wrocław, Poland |
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| Abstract: | Let X be a Banach space with a Schauder basis {e
n
}, and let Φ(I) = Σ
n=1∞
e
n
∫
I
f
n
(t)dt be a finitely additive interval measure on the unit interval 0, 1], where the integrals are taken in the sense of Henstock-Kurzweil.
Necessary and sufficient conditions are given for Φ to be the indefinite integral of a Henstock-Kurzweil-Pettis (or Henstock,
or variational Henstock) integrable function f: 0, 1] → X. |
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| Keywords: | Henstock Kurzweil integral Henstock-Kurzweil-Pettis integral Henstock integral variational Henstock integral Pettis integral |
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