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

We study some Banach lattice properties of the space L-w(1)(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 L-w(1)(v) differs from the case in which is defined on a sigma-algebra whenever does not satisfy certain local sigma-finiteness property.J. M. Calabuig and M. A. Juan were supported by the Ministerio de Economia y Competitividad (project MTM2008-04594). O. Delgado was supported by the Ministerio de Economia y Competitividad (project MTM2009-12740-C03-02). E. A. Sanchez Perez was supported by the Ministerio de Economia y Competitividad (project MTM2009-14483-C02-02).Calabuig Rodriguez, JM.; Delgado Garrido, O.; Juan Blanco, MA.; Sánchez Pérez, EA. (2014). On the Banach lattice structure of L-w(1) of a vector measure on a delta-ring. Collectanea Mathematica. 65(1):67-85. doi:10.1007/s13348-013-0081-8S678565