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Filter Convergence and Decompositions for Vector Lattice-Valued Measures

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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, obtained in Boccuto et al. (Math Slovaca 62(6):1145–1166, 2012), is used.

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Authors and Affiliations

  1. Dipartimento di Matematica e Informatica, via Vanvitelli 1, 06123, Perugia, Italy

    Domenico Candeloro & Anna Rita Sambucini

Authors
  1. Domenico Candeloro
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  2. Anna Rita Sambucini
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Correspondence to Domenico Candeloro.

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Dedicated to Prof. Benedetto Bongiorno

The authors have been partially supported by University of Perugia—Department of Mathematics and Computer Sciences, Prin “Descartes”, Prin “Metodi logici per il trattamento dell’ informazione” and by the Grant prot. U2014/000237 of GNAMPA-INDAM (Italy).

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Candeloro, D., Sambucini, A.R. Filter Convergence and Decompositions for Vector Lattice-Valued Measures. Mediterr. J. Math. 12, 621–637 (2015). https://doi.org/10.1007/s00009-014-0431-0

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  • DOI: https://doi.org/10.1007/s00009-014-0431-0

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