Convergence of a sequence of weakly regular set functions
J. Dieudonné proved that if a sequence of regular Borelian measures converges on the system of open subsets of a compact metric space \(X\), then it converges on all Borelian subsets of \(X\). This theorem has been generalized by many authors, e.g., by A. Grothendieck (for \(X\) being locally compact) or by P.~Gänssler (for a regular Hausdorff space \(X\)). In this paper the authors prove an analogous theorem for set functions that are weakly regular, non-additive, defined on some algebra of sets which contains the class of open subsets of an arbitrary \(\sigma\)-topological space \(X\), and take values in a uniform space.
scientific article; zbMATH DE number 1256797