Proceedings of the Edinburgh Mathematical Society (Series 2)

Table of Contents - February 1990 - Volume 33, Issue 01  

Research Article

Completeness of the L1-space of closed vector measures

Werner J. Rickera1 p1

a1 Fachbereich Mathematik, Universität des Saarlandes, D-6600 Saarbrücken, Federal Republic of Germany

Abstract

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)

Correspondence:

p1 School of Mathematics, University of New South Wales, Kensington, NSW, 2033, Australia