Equivalence between limit theorems for lattice group-valued \(k\)-triangular set functions. (English) Zbl 1400.28004
Summary: We investigate some of the main properties of lattice group-valued \(k\)-triangular set functions and we prove some Brooks-Jewett, Nikodým, Vitali-Hahn-Saks and Schur-type theorems and their equivalence. A Drewnowski-type theorem on existence of continuous restrictions of (\(s\))-bounded set functions is given.
MSC:
| 28A12 | Contents, measures, outer measures, capacities |
| 26E50 | Fuzzy real analysis |
| 28A33 | Spaces of measures, convergence of measures |
| 28B10 | Group- or semigroup-valued set functions, measures and integrals |
| 28B15 | Set functions, measures and integrals with values in ordered spaces |
| 46G10 | Vector-valued measures and integration |
Keywords:
lattice group; \(k\)-triangular set function; continuous set function; (\(s\))-bounded set function; Fremlin lemma; limit theoremReferences:
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