Equivalence between limit theorems for lattice group-valued k-triangular set functions
Antonio Boccuto, Xenofon Dimitriou
TL;DR
This paper explores the properties of lattice group-valued k-triangular set functions, establishing key theorems and their equivalence, and providing conditions for continuous restrictions of bounded set functions.
Contribution
It introduces new equivalence results among classical theorems for lattice group-valued set functions and proves a Drewnowski-type theorem on continuous restrictions.
Findings
Proved Brooks-Jewett, Nikodym, Vitali-Hahn-Saks, and Schur-type theorems and their equivalence.
Established a Drewnowski-type theorem for continuous restrictions of (s)-bounded set functions.
Analyzed properties of lattice group-valued k-triangular set functions.
Abstract
We investigate some main properties of lattice group-valued k-triangular set functions and prove some Brooks-Jewett, Nikodym, 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.
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Taxonomy
TopicsAdvanced Banach Space Theory · Approximation Theory and Sequence Spaces · Functional Equations Stability Results