Authors:Christopher Boyd, Seán Dineen, and Pilar Rueda
Defant  introduced the local Radon–Nikodým property for duals of locally convex spaces. This is a generalization of Asplund
spaces as defined in Banach space theory. In this paper we generalise Dunford"s Theorem  to Banach spaces with Schauder
decompositions and apply this result to spaces of holomorphic functions on balanced domains in a Banach space.
Motivated by the well known Kadec-Pełczynski disjointification theorem, we undertake an analysis of the supports of non-zero functions in strongly embedded subspaces of Banach functions spaces. The main aim is to isolate those properties that bring additional information on strongly embedded subspaces. This is the case of the support localization property, which is a necessary condition fulfilled by all strongly embedded subspaces. Several examples that involve Rademacher functions, the Volterra operator, Lorentz spaces or Orlicz spaces are provided.