On the Banach lattice structure of L-w(1) of a vector measure on a delta-ring

Calabuig Rodriguez Jose Manuel, Delgado Garrido Olvido, Juan Blanco María Aránzazu, Sánchez Pérez Enrique Alfonso

2014

Collectanea mathematica

We study some Banach lattice properties of the space L1w)(v) of weakly integrable functions with respect to a vector measure v defined on a delta-ring. Namely, we analyze order continuity, order density and Fatou type properties. We will see that the behavior of L1w(ν) differs from the case in which ν is defined on a σ-algebra whenever ν does not satisfy certain local σ-finiteness property.