Cafiero approach to the Dieudonné type theorems

Abstract

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.