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

Boccuto, Antonio ; Dimitriou, Xenofon

Kybernetika, Tome 55 (2019) no. 2, pp. 233-251

Abstract (VO)

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.

Détail

DOI : 10.14736/kyb-2019-2-0233

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

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