Equivalence between limit theorems for 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, 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. Furthermore we pose some open problems.