Some new results on ideal limit theorems in l-groups

We present some limit theorems for sequences of measures, taking values in l-groups, in the setting of ideal convergence. We use the tool of ideal exhaustiveness in order to prove some results on uniform s-boundedness, uniform sigma-additivity, uniform absolute continuity and uniform regularity of a suitable subsequence of the given one, whose indexes belong to the dual filter associated to the ideal involved. We observe that, in general, ideal exhaustiveness is a condition, which cannot be dropped and we give an example about it. We deal with Frechet-Nikodym topologies and submeasures.