Radon-Nikodym derivatives for vector measures belonging to Kothe function spaces

Let m, n be a couple of vector measures with values on a Banach space. We develop a separation argument which provides a characterization of when the Raclon-Nikodym derivative of n with respect to m-in the sense of the Bartle-Dunford-Schwartz integral-exists and belongs to a particular sublattice Z(mu) of the space of integrable functions L I (m). We show that this theorem is in fact a particular feature of our separation argument, which can be applied to prove other results in both the vector measure and the function space settings. (C) 2008 Elsevier Inc. All rights reserved.