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