a1 Fachbereich Mathematik, Universität des Saarlandes, D-6600 Saarbrücken, Federal Republic of Germany
The notion of a closed vector measure m, due to I. Kluv´;nek, is by now well established. Its importance stems from the fact that if the locally convex space X in which m assumes its values is sequentially complete, then m is closed if and only if its L1-space is complete for the topology of uniform convergence of indefinite integrals. However, there are important examples of X-valued measures where X is not sequentially complete. Sufficient conditions guaranteeing the completeness of L1(m) for closed X-valued measures m are presented without the requirement that X be sequentially complete.
(Received April 04 1988)
p1 School of Mathematics, University of New South Wales, Kensington, NSW, 2033, Australia