J. Aust. Math. Soc.
82 (2007), 85109

Spaces of vector functions that are integrable with respect to vector measures

José Rodríguez
Departamento de Matemáticas
Universidad de Murcia
30.100 Espinardo
Murcia
Spain
joserr@um.es



Abstract

We study the normed spaces of (equivalence
classes of) Banach spacevalued functions that
are Dobrakov, S^{*}
or McShane integrable with respect to a Banach
spacevalued measure, where the norm is the
natural one given by the total semivariation of
the indefinite integral. We show that simple
functions are dense in these spaces. As a
consequence we characterize when the
corresponding indefinite integrals have norm
relatively compact range. On the other hand, we
also determine when these spaces are
ultrabornological. Our results apply to
conclude, for instance, that the spaces of
Birkhoff (respectively McShane) integrable
functions defined on a complete (respectively
quasiRadon) probability space, endowed with
the Pettis norm, are ultrabornological.

Download the article in PDF format (size 264 Kb)


Australian Mathematical Publishing Association Inc.

©
Australian MS

