Some Brooks-Jewett, Vitali-Hahn-Saks and Nikodym convergence-type theorems in the context of l-groups with respect to ideal convergence are proved. Moreover, an example is given, in which it is shown that in general results analogous to these kinds of limit theorems do not hold, when pointwise convergence of the measure involved is replaced by the corresponding ideal pointwise convergence.
Brooks-Jewett-type theorems for the pointwise ideal convergence of measures with values in l-groups
BOCCUTO, Antonio;
2011
Abstract
Some Brooks-Jewett, Vitali-Hahn-Saks and Nikodym convergence-type theorems in the context of l-groups with respect to ideal convergence are proved. Moreover, an example is given, in which it is shown that in general results analogous to these kinds of limit theorems do not hold, when pointwise convergence of the measure involved is replaced by the corresponding ideal pointwise convergence.File in questo prodotto:
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