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arXiv · 1401.7818

Filter convergence and decompositions for vector lattice-valued measures

Domenico Candeloro·Anna Rita Sambucini
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Abstract

Filter convergence of vector lattice-valued measures is considered, in order to deduce theorems of convergence for their decompositions. First the $σ$-additive case is studied, without particular assumptions on the filter; later the finitely additive case is faced, first assuming uniform $s$-boundedness (without restrictions on the filter), then relaxing this condition but imposing stronger properties on the filter. In order to obtain the last results, a Schur-type convergence theorem is used.

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Domenico Candeloro, Anna Rita Sambucini. 2014-01-30. Filter convergence and decompositions for vector lattice-valued measures. https://doi.org/10.1007/s00009-014-0431-0

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