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Cafiero approach to Dieudonne's type theorems 2008 http://ezaposleni.singidunum.ac.rs/rest/sciNaucniRezultati/oai/record/2/1927 http://www.journals.elsevier.com/journal-of-mathematical-analysis-and-applications/ P. de Lucia E. Pap 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. article 337 2 1151 1157 0022-247X JOURNAL OF MATHEMATICAL ANALYSIS AND APPLICATIONS