We prove that sharply dominating Archimedean atomic lattice effect algebras can be characterized by the property called basic decomposition of elements.As an application we prove the state smearing theorem for these effect algebras.
We prove a unified convergence theorem, which presents, in four equivalentforms, the famous Antosik-Mikusinski theorems. In particular, we show that Swartz' three uniformconvergence principles are all equivalent to the Antosik-Mikusinski theorems.
