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


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.


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


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


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