Boccuto, A.; Candeloro, D. Dieudonné-type theorems for set functions with values in \((l)\)-groups. (English) Zbl 1067.28011 Real Anal. Exch. 27(2001-2002), No. 2, 473-483 (2002). A theorem of Dieudonné essentially says that an equibounded sequence of regular \(\sigma\)-additive real-valued measures converging on all open sets converges on all Borel sets and that the limit function is a regular \(\sigma\)-additive measure. The authors generalize this theorem for \(l\)-group-valued measures. A crucial point is here the use of a suitable convergence in \(l\)-groups. Moreover, the authors replace the system of open and the system of closed sets by abstract lattices. Reviewer: Hans Weber (Udine) Cited in 7 Documents MSC: 28B15 Set functions, measures and integrals with values in ordered spaces 28B10 Group- or semigroup-valued set functions, measures and integrals 46G10 Vector-valued measures and integration Keywords:\(l\)-group-valued measures; Dieudonné theorems; Vitali-Hahn-Saks theorems PDFBibTeX XMLCite \textit{A. Boccuto} and \textit{D. Candeloro}, Real Anal. Exch. 27, No. 2, 473--483 (2002; Zbl 1067.28011) Full Text: DOI