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International Journal of Mathematical Analysis and Applications

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Disjoint Variation, (s)-Boundedness and Brooks-Jewett Theorems for Lattice Group-Valued k-Triangular Set Functions

International Journal of Mathematical Analysis and Applications
Vol.3 , No. 3, Publication Date: Sep. 13, 2016, Page: 26-30

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Authors

[1]	A. Boccuto, Dipartimento di Matematica e Informatica, University of Perugia, Perugia, Italy.

Abstract

We consider some basic properties of the disjoint variation of lattice group-valued set functions and (s)-boundedness for k-triangular set functions, not necessarily finitely additive or monotone. Using the Maeda-Ogasawara-Vulikh representation theorem of lattice groups as subgroups of continuous functions, we prove a Brooks-Jewett-type theorem for k-triangular lattice group-valued set functions, in which (s)-boundedness is intended in the classical like sense, and not necessarily with respect to a single order sequence. To this aim, we deal with the disjoint variation of a lattice group-valued set function and study the basic properties of the set functions of bounded disjoint variation. Furthermore we show that our setting includes the finitely additive case.

Keywords

Lattice Group, Triangular Set Function, (Bounded) Disjoint Variation, Brooks-Jewett Theorem

Reference

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