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2011/2012 Limit Theorems in (l)-Groups with Respect to (D)-Convergence
Antonio Boccuto, Xenofon Dimitriou, Nikolaos Papanastassiou
Real Anal. Exchange 37(2): 249-278 (2011/2012).


Some Schur, Vitali-Hahn-Saks and Nikodým convergence theorems for \((l)\)-group-valued measures are given in the context of \((D)\)-convergence. We consider both the \(\sigma\)-additive and the finitely additive case. Here the notions of strong boundedness, countable additivity and absolute continuity are formulated not necessarily with respect to a same regulator, while the pointwise convergence of the measures is intended relatively to a common \((D)\)-sequence. Among the tools, we use the Fremlin lemma, which allows us to replace a countable family of \((D)\)-sequence with one regulator, and the Maeda-Ogasawara-Vulikh representation theorem for Archimedean lattice groups.


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Antonio Boccuto. Xenofon Dimitriou. Nikolaos Papanastassiou. "Limit Theorems in (l)-Groups with Respect to (D)-Convergence." Real Anal. Exchange 37 (2) 249 - 278, 2011/2012.


Published: 2011/2012
First available in Project Euclid: 15 April 2013

zbMATH: 1260.28010
MathSciNet: MR3080590

Primary: 28B15
Secondary: 28B05

Keywords: (D)-sequence , Fremlin lemma , l-group , Maeda-Ogasawara-Vulikh theorem , Nikodym convergence theorem , Schur lemma , Vitali-Hahn-Saks theorem

Rights: Copyright © 2011 Michigan State University Press

Vol.37 • No. 2 • 2011/2012
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