TITLE:
Nikodým-Type Theorems for Lattice Group-Valued Measures with Respect to Filter Convergence
AUTHORS:
Antonio Boccuto, Xenofon Dimitriou
KEYWORDS:
Lattice Group, (Free) Filter, (s)-Bounded Measure, σ-Additive Measure, Diagonal Filter, Block-Respecting Filter, Limit Theorem, Nikodým Boundedness Theorem
JOURNAL NAME:
Advances in Pure Mathematics,
Vol.4 No.5,
May
16,
2014
ABSTRACT:
We
present some convergence and boundedness theorems with respect to filter
convergence for lattice group-valued measures. We give a direct proof, based on
the sliding hump argument. Furthermore we pose some open problems.