Journal of the Australian Mathematical Society - Series A
Vol. 64 Part 2 (1998)

Rybakov's theorem in Fréchet spaces and completeness of L^{1}-spaces

W. J. Ricker
School of Mathematics
University of New South Wales
Sydney, NSW 2052
Australia

Abstract:

We provide a simple and direct proof of the
completeness of the L^{1}-space of any vector measure taking its
values in the class of Fréchet spaces which do not contain a copy
of the sequence space .