This is an announcement for the paper "Filter convergence and decompositions for vector lattice-valued" by Domenico Candeloro and Anna Rita Sambucini.

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.

Archive classification: math.FA

Mathematics Subject Classification: 28B15, 28B05, 06A06, 54F05

Report Number: 0901688 30 jan 2014

Remarks: 18 pages

Submitted from: anna.sambucini@unipg.it

The paper may be downloaded from the archive by web browser from URL

http://front.math.ucdavis.edu/1401.7818

or

http://arXiv.org/abs/1401.7818