Vitali-Hahn-Saks and Nikodym theorems for means with values in Riesz spaces

In this paper we prove some versions of limit theorems (Brooks-Jewett, Vitali-Hahn-Saks and Nikodym convergence theorems) for Riesz space-valued measures, strongly bounded, absolutely continuous and countably additivity respectively. Using the Maeda-Ogasawara-Vulikh representation theorem, we first prove some limit theorems in the case in which the limit measure satisfies some "good" property (sigma-additivity or absolute continuity) and the involved measure are positive. Moreover, after requiring supplementary hypotheses for the limit measure, we prove some limit theorems for positive measures, taking values in suitable subspaces of L^0.