Abstract
For V a Nachbin family, on a zero-dimensional Hausdorff topological space X, and E a non-Archimedean Hausdorff locally convex space, it is shown that the dual spaces of the Nachbin spaces CV0(X) and CV0(X, E) are algebraically isomorphic to certain spaces of measures on a ring of subsets of X. Also, the space of all continuous linear maps, from CV0(X, E) to another locally convex space F, is algebraically isomorphic to a space of L(E, F)-valued measures. (C) 2012 Royal Dutch Mathematical Society (KWG). Published by Elsevier B.V. All rights reserved.