On the Banach lattice structure of L^1_w of a vector measure on a \delta-ring

• Autores: José Manuel Calabuig Rodríguez , Olvido Delgado Garrido , M.A. Juan, Enrique Alfonso Sánchez Pérez
• Localización: Collectanea mathematica, ISSN 0010-0757, Vol. 65, Fasc. 1, 2014, págs. 67-85
• Idioma: inglés
• DOI: 10.1007/s13348-013-0081-8
• Texto completo no disponible (Saber más ...)
• Resumen

  • We study some Banach lattice properties of the space L_w^1(\nu ) of weakly integrable functions with respect to a vector measure \nu 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(\nu ) differs from the case in which \nu is defined on a \sigma-algebra whenever \nu does not satisfy certain local \sigma-finiteness property.