A characterization of Banach spaces possessing the Radon–Nikodým property is given in terms of finitely additive interval functions. We prove that a Banach space $X$ has the RNP if and only if each $X$-valued finitely additive interval function possessing absolutely continuous variational measure is a variational Henstock integral of an $X$-valued function. Due to that characterization several $X$-valued set functions that are only finitely additive can be represented as integrals.
"A variational Henstock integral characterization of the Radon–Nikodým property." Illinois J. Math. 53 (1) 87 - 99, Spring 2009. https://doi.org/10.1215/ijm/1264170840