Independence and convergence in non-additive settings

Some properties of convergence for archimedean t-conorms and t-norms are investigated and a definition of independence for events, evaluated by a decomposable measure, is introduced. This definition generalizes the concept of independence provided by Kruse and Qiang for λ-additive fuzzy measures. Finally, we derive the two Borel–Cantelli lemmas in the context of the general framework considered.