Abstract and Applied Analysis
Volume 4 (1999), Issue 4, Pages 209-229

A Riesz representation theorem for cone-valued functions

Walter Roth

Department of Mathematics, Universiti Brunei Darussalam, Gadong BE 1410, Brunei Darussalam

Received 29 November 1999

Copyright © 1999 Walter Roth. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We consider Borel measures on a locally compact Hausdorff space whose values are linear functionals on a locally convex cone. We define integrals for cone-valued functions and verify that continuous linear functionals on certain spaces of continuous cone-valued functions endowed with an inductive limit topology may be represented by such integrals.