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

Autores UPV
Revista 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.