JID:FSS AID:6834 /FLA [m3SC+; v1.207; Prn:26/06/2015; 13:04] P.1(1-21) Available online at www.sciencedirect.com ScienceDirect Fuzzy Sets and Systems ••• (••••) •••–••• www.elsevier.com/locate/fss Pseudo-D-lattices and separating points of measures Anna Avallone, Paolo Vitolo ∗ Dipartimento di Matematica, Informatica ed Economia, Università della Basilicata, Viale dell’Ateneo Lucano, 10, 85100 Potenza, Italy Received 27 January 2015; received in revised form 8 May 2015; accepted 19 June 2015 Abstract 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 G δ -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 ∈ M are distinct, the quotient of R modulo 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.  2015 Elsevier B.V. All rights reserved. Keywords: Mathematics; Analysis; Measure theory 0. Introduction A question which has been studied in classical Measure Theory is to establish when a family M of measures on a Boolean ring R admits a separating point, i.e. a point a ∈ R such that μ(a)  = ν(a) for all pairs {μ, ν } of different members of M . In this respect, A. Basile and H. Weber in [11] considered, on a Boolean ring R, a countable family M of measures and a topology τ which makes them continuous. In order to prove that the set S M of separating points for M is nonempty, their task was to establish sufficient conditions under which it is a dense G δ -set with respect to τ , assuming that M is finite or that R is σ -complete and every measure in M is σ -additive. Their conditions are: (i) each element of M is s-bounded (i.e. exhaustive) and, whenever λ, ν ∈ M are distinct, the quotient R/N(λ − ν) is infinite, or (ii) each element of M is continuous (i.e. nonatomic). A similar result has been proved in [2] for orthomodular lattices. More precisely, due to the lack of distributivity, condition (i) becomes: each element of M is exhaustive and, whenever λ, ν ∈ M are distinct, the quotient modulo N(λ − ν) contains an infinite chain. Some years later, in the article [1], the problem of separating points is investigated in the more general situation of modular measures on D-lattices (i.e. lattice-ordered effect algebras). * Corresponding author. E-mail addresses: anna.avallone@unibas.it (A. Avallone), paolo.vitolo@unibas.it (P. Vitolo). http://dx.doi.org/10.1016/j.fss.2015.06.015 0165-0114/ 2015 Elsevier B.V. All rights reserved.