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Convergence and decompositions for 1-group-valued set functions

100%

Boccuto A. , Candeloro D.

tom Vol. 44, nr 1

11--38

Absolute continuity, singularity and Lebesgue decompositions are studied, in the context of the so-called RD-convergence, for finitely and/or σ-additive measures taking values in super-Dedekind complete l-groups. By means of a Vitali-Hahn-Saks-Nikodým result, found in [4], we deduce a convergence theorem for the Lebesgue decompositions of an RD-convergent sequence of finitely additive measures.

Modes of ideal continuity and the additive property in the Riesz space setting

80%

Boccuto A. , Dimitriou X. , Papanastassiou N. , Wilczyński W.

tom Vol. 20, nr 1

41--53

In this paper we present some different types of ideal convergence/divergence and of ideal continuity for Riesz space-valued functions, and prove some basic properties and comparison results. We investigate the relations among different modes of ideal continuity and present a characterization of the (AP)-property for ideals of an abstract set Λ. Finally we pose some open problems.

Unconditional convergence in lattice groups with respect to ideals

80%

Boccuto A. , Dimitriou X. , Papanastassiou N.

tom Vol. 50, [Z] 2

161-174

We deal with unconditional convergence of series and some special classes of subsets of N.