Some new results about Brooks-Jewett and Dieudonné-type theorems in l-groups

In this paper we present some new versions of Brooks-Jewett and Dieudonne'-type theorems for l-group-valued measures. Here the concepts of s-boundedness, sigma-additivity and regularity are formulated similarly as in the classical case, and not directly related to order sequences, regulators or similar objects. We use the tools of the Maeda-Ogasawara-Vulikh representation theorem and a technical lemma, which allows to prove some properties of l-group-valued measures using the corresponding ones of real-valued set functions.