The Fatou property in p-convex Banach lattices ✩

New features of the Banach function space L p w(ν), that is, the space of all ν-scalarly pth power integrable functions (with 1 p <∞and ν any vector measure), are presented. The Fatou property plays an essential role and leads to a new representation theorem for a large class of abstract p-convex Banach lattices. © 2006 Elsevier Inc. All rights reserved