Pseudo-D-lattices and separating points of measures

In 1986, A. Basile and H. Weber proved that every countable family M of σ-additive measures on a σ-complete Boolean ring R   admits a dense GδGδ-set of separating points, with respect to a suitable topology, in the following two cases: either (i) each element of M   is s-bounded and, whenever λ,ν∈Mλ,ν∈M are distinct, the quotient of R   modulo N(λ−ν)N(λ−ν) is infinite, or (ii) each element of M is continuous. In this paper we consider modular measures on lattice-ordered pseudo-effect algebras. Using topological methods, we extend the result of Basile and Weber in a way that allows to unify the above two cases (i) and (ii). This gives a new contribution also in the classical setting of algebras of sets.