Limit Theorems for k-Subadditive Lattice Group-Valued Capacities in The Filter Convergence Setting

Antonio Boccuto; Xenofon Dimitriou

doi:10.1515/tmmp-2016-0001

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Limit Theorems for k-Subadditive Lattice Group-Valued Capacities in The Filter Convergence Setting

Tatra Mountains Mathematical Publications

Volume 65 (2016): Issue 1 (March 2016)

By: Antonio Boccuto and Xenofon Dimitriou

Open Access

|Aug 2016

Abstract

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.

References

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Articles in this issue

DOI: https://doi.org/10.1515/tmmp-2016-0001 | Journal eISSN: 1338-9750 | Journal ISSN: 1210-3195

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Language: English

Page range: 1 - 21

Submitted on: Oct 20, 2014

Published on: Aug 4, 2016

Published by: Slovak Academy of Sciences, Mathematical Institute

In partnership with: Paradigm Publishing Services

Publication frequency: 1 issue per year

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,

Related subjects:

© 2016 Antonio Boccuto, Xenofon Dimitriou, published by Slovak Academy of Sciences, Mathematical Institute
This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 4.0 License.

Volume 65 (2016): Issue 1 (March 2016)