Radon-Nikodým derivatives for vector measures belonging to Köthe function spaces

Abstract

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 Radon-Nikodým derivative of n with respect to m-in the sense of the Bartle-Dunford-Schwartz integral-exists and belongs to a particular sublattice Z (μ) of the space of integrable functions L¹ (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. © 2008 Elsevier Inc. All rights reserved.