We present a complete characterization of finitely additive interval measures with values in conjugate Banach spaces which can be represented as Henstock-Kurzweil-Gelfand integrals. If the range space has the weak Radon-Nikodym property (WRNP), then we precisely describe when these integrals are in fact Henstock-Kurzweil-Pettis integrals.
Bongiorno, B., Di Piazza, L., Musial, K. (2014). Differentiation of an additive interval measure with values in a conjugate Banach space. FUNCTIONES ET APPROXIMATIO COMMENTARII MATHEMATICI, 50(50.1), 169-180 [DOI: 10.7169/facm/2014.50.1.6.].
Differentiation of an additive interval measure with values in a conjugate Banach space
DI PIAZZA, Luisa;
2014-01-01
Abstract
We present a complete characterization of finitely additive interval measures with values in conjugate Banach spaces which can be represented as Henstock-Kurzweil-Gelfand integrals. If the range space has the weak Radon-Nikodym property (WRNP), then we precisely describe when these integrals are in fact Henstock-Kurzweil-Pettis integrals.
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