Ultrapowers of spaces of integrable functions with respect to a sequential vector measure and locally bounded sets of functions

Consider the space of functions that are integrable with respect to a vector measure. In this paper we deal with such spaces defined using a particular class of measures that we call sequential vector measures. We prove that these spaces always define complemented subspaces of their ultrapowers. We use this result to characterize increase properties of certain families of functions by mean of the related projection.  2003 Elsevier Inc. All rights reserved