Dieudonné-type theorems for lattice group-valued k -triangular set functions

Antonio Boccuto; Xenofon Dimitriou

Kybernetika (2019)

  • Volume: 55, Issue: 2, page 233-251
  • ISSN: 0023-5954

Abstract

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Some versions of Dieudonné-type convergence and uniform boundedness theorems are proved, for k -triangular and regular lattice group-valued set functions. We use sliding hump techniques and direct methods. We extend earlier results, proved in the real case. Furthermore, we pose some open problems.

How to cite

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Boccuto, Antonio, and Dimitriou, Xenofon. "Dieudonné-type theorems for lattice group-valued $k$-triangular set functions." Kybernetika 55.2 (2019): 233-251. <http://eudml.org/doc/294748>.

@article{Boccuto2019,
abstract = {Some versions of Dieudonné-type convergence and uniform boundedness theorems are proved, for $k$-triangular and regular lattice group-valued set functions. We use sliding hump techniques and direct methods. We extend earlier results, proved in the real case. Furthermore, we pose some open problems.},
author = {Boccuto, Antonio, Dimitriou, Xenofon},
journal = {Kybernetika},
keywords = {lattice group; $(D)$-convergence; $k$-triangular set function; $(s)$-bounded set function; Fremlin lemma; limit theorem; Brooks–Jewett theorem; Dieudonné theorem; Nikodým boundedness theorem},
language = {eng},
number = {2},
pages = {233-251},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Dieudonné-type theorems for lattice group-valued $k$-triangular set functions},
url = {http://eudml.org/doc/294748},
volume = {55},
year = {2019},
}

TY - JOUR
AU - Boccuto, Antonio
AU - Dimitriou, Xenofon
TI - Dieudonné-type theorems for lattice group-valued $k$-triangular set functions
JO - Kybernetika
PY - 2019
PB - Institute of Information Theory and Automation AS CR
VL - 55
IS - 2
SP - 233
EP - 251
AB - Some versions of Dieudonné-type convergence and uniform boundedness theorems are proved, for $k$-triangular and regular lattice group-valued set functions. We use sliding hump techniques and direct methods. We extend earlier results, proved in the real case. Furthermore, we pose some open problems.
LA - eng
KW - lattice group; $(D)$-convergence; $k$-triangular set function; $(s)$-bounded set function; Fremlin lemma; limit theorem; Brooks–Jewett theorem; Dieudonné theorem; Nikodým boundedness theorem
UR - http://eudml.org/doc/294748
ER -

References

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