Article
MSC:
28A12,
28A33,
28B10,
28B15,
40A35,
46G10 | MR 4014585 | Zbl 07144936 | DOI: 10.14736/kyb-2019-2-0233
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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
lattice group; $(D)$-convergence; $k$-triangular set function; $(s)$-bounded set function; Fremlin lemma; limit theorem; Brooks–Jewett theorem; Dieudonné theorem; Nikodým boundedness theorem
Summary:
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.
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