Kybernetika 55 no. 2, 233-251, 2019

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

Antonio Boccuto and Xenofon DimitriouDOI: 10.14736/kyb-2019-2-0233

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.

Keywords:

Dieudonné theorem, limit theorem, lattice group, $(D)$-convergence, $k$-triangular set function, $(s)$-bounded set function, Fremlin lemma, Brooks-Jewett theorem, Nikodým boundedness theorem

Classification:

28A12, 28A33, 28B10, 28B15, 40A35, 46G10

paper.pdf

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