Completeness of L-1-spaces for measures with values in complex vector spaces

摘要

We provide a simple and direct proof of the completeness of the space of C-valued integrable functions with respect to a vector measure taking its values in a complex Frechet space. A similar result is established (via a quite different argument) for closed measures taking their values in more general sequentially complete, locally convex Hausdorff spaces over C. (C) 1998 Academic Press. [References: 8]