Measure theory in Naples; Renato Caccioppoli
The author discusses one of the important directions of concern in Renato Caccioppoli's mathematical work, namely the problem of uniform additivation. The reason for this selection is, on one hand, the special interest paid to such problems lately, by the present-day Italian mathematicians and, on the other hand, the fact that a symposium devoted to uniform additivity was organized by Federico Cafiero, in 1968, as a homage to the memory of Caccioppoli. Ample space is devoted to the definition of the family of functions with uniformly limited variations, the interpretation given by Caccioppoli and the directions his ideas opened in modern mathematics, as to this topic, being underlined and commented upon thoroughly. Mention is made of the fact that the notion of family of functions with uniformly limited variations is to be met, later, in the work of a Russian mathematician, V. M. Dubrovskij. Also, Cafiero devoted several studies to this problem, putting forth a special criterion, based on which the classical theorems of convergence of Nikodym and Vitali-Hahn-Saks may be deduced.
scientific article; zbMATH DE number 510080