Limit Theorems for k-Subadditive Lattice Group-Valued Capacities in The Filter Convergence Setting
and | Aug 04, 2016
Tatra Mountains Mathematical Publications
Real Functions '15 — Measure Theory, Real Functions, General Topology. Editors: J. Borsík, 2016.
About this article
Published Online: Aug 04, 2016
Page range: 1 - 21
Received: Oct 20, 2014
DOI: https://doi.org/10.1515/tmmp-2016-0001
Keywords
lattice group, (diagonal) filter, filter (D)-convergence, filter (O)-convergence, k-subadditive capacity, continuous capacity, regular capacity, (s)-bounded capacity, Fremlin’s lemma, Maeda-Ogasawara-Vulikh theorem, limit theorem, Brooks-Jewett theorem, Vitali- -Hahn-Saks theorem, Nikod´ym theorem, Dieudonn´e theorem
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We investigate some properties of lattice group-valued positive, monotone and k-subadditive set functions, and in particular, we give some comparisons between regularity and continuity from above. Moreover, we prove different kinds of limit theorems with respect to filter convergence. Furthermore, some open problems are posed.