A variational Henstock integral characterization of the Radon-Nikodym property

A characterization of Banach spacespossessing the Radon-Nikodym property is given in terms offinitely additive interval functions. We prove that a Banach spaceX has the RNP if and only if each X-valued finitely additiveinterval function possessing absolutely continuous variationalmeasure is a variational Henstock integral of an X-valuedfunction. Due to that characterization several X-valued setfunctions that are only finitely additive can be represented asintegrals.