Let X be a Banach space with a Schauder basis {en}, and let Φ(I)= ∑n en ∫I fn(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.
Bongiorno, B., Di Piazza, L., Musial, K. (2012). Radon-Nikodym derivatives of finitely additive interval measures taking values in a Banach space with basis. ACTA MATHEMATICA SINICA, 28 (2), 219-234 [10.1007/s10114-011-0614-6].
Radon-Nikodym derivatives of finitely additive interval measures taking values in a Banach space with basis
BONGIORNO, Benedetto;DI PIAZZA, Luisa;
2012-01-01
Abstract
Let X be a Banach space with a Schauder basis {en}, and let Φ(I)= ∑n en ∫I fn(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.
File in questo prodotto:
Non ci sono file associati a questo prodotto.
I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
