Schur lemma and limit theorems in lattice groups with respect to filters

Some Schur, Nikodým, Brooks-Jewett and Vitali-Hahn-Saks-type theorems for (ℓ)-group-valued measures are proved in the setting of filter convergence. Finally we pose an open problem.

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Bibliographic Details
Published in:Mathematica Slovaca 2012-12, Vol.62 (6), p.1145-1166
Main Authors: Boccuto, A., Dimitriou, X., Papanastassiou, N.
Format: Article
Language:English
Subjects:
(D)-sequence
(ℓ)-group
Algebra
Brooks-Jewett theorem
filter
filter convergence
Fremlin lemma
Mathematics
Mathematics and Statistics
Nikodým convergence theorem
order sequence
Primary 28B15
Regular Papers
Schur lemma
Secondary 54A20
Vitali-Hahn-Saks theorem
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Description
Summary:Some Schur, Nikodým, Brooks-Jewett and Vitali-Hahn-Saks-type theorems for (ℓ)-group-valued measures are proved in the setting of filter convergence. Finally we pose an open problem.
ISSN:0139-9918
1337-2211
DOI:10.2478/s12175-012-0070-5