Some limit and Dieudonné-type theorems in the setting of l-groups with respect to filter convergence are proved, extending earlier results. A particular importance is given to (uniform) absolute continuity and (uniform) regular measures. We deal with pointwise filter convergence, and by studying "good countability properties" of filters involved we are able to reconduct some properties of ideal convergence (which is weaker than the classical one) to some corresponding properties of the usual convergence, in order to prove our results.
Some versions of limit and Dieudonné-type theorems with respect to filter convergence for l-group-valued measures
BOCCUTO, Antonio;
2011
Abstract
Some limit and Dieudonné-type theorems in the setting of l-groups with respect to filter convergence are proved, extending earlier results. A particular importance is given to (uniform) absolute continuity and (uniform) regular measures. We deal with pointwise filter convergence, and by studying "good countability properties" of filters involved we are able to reconduct some properties of ideal convergence (which is weaker than the classical one) to some corresponding properties of the usual convergence, in order to prove our results.File in questo prodotto:
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