Differentiation of an additive interval measure with values in a conjugate Banach space

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