Cafiero approach to the Dieudonné type theorems

An algebra of subsets of a normal topological space containing the open sets is considered and in this context the uniform exhaustivity and uniform regularity for a family of additive functions are studied. Based on these results the Cafiero convergence theorem with the Dieudonné type conditions is proved and in this way also the Nikodým–Dieudonné convergence theorem is obtained. © 2007 Elsevier Inc. All rights reserved.