Filter convergence and decompositions for vector lattice-valued measures

Abstract

Filter convergence of vector lattice-valued measures is considered, in order to deduce theorems of convergence for their decompositions. First the $\sigma$-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.

18 pages

References in corpus (1)

• Vitali-type theorems for filter convergence related to vector lattice-valued modulars and applications to stochastic processes

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