Embeddings of metric Boolean algebras in [formula omitted].

A Boolean algebra A equipped with a (finitely-additive) positive probability measure m can be turned into a metric space (A , d m) , where d m (a , b) = m ((a ∧ ¬ b) ∨ (¬ a ∧ b)) , for any a , b ∈ A , sometimes referred to as metric Boolean algebra. In this paper, we study under which conditions the space of atoms of a finite metric Boolean algebra can be isometrically embedded in R N (for a certain N) equipped with the Euclidean metric. In particular, we characterize the topology of the positive measures over a finite algebra A such that the metric space (At (A) , d m) embeds isometrically in R N (with the Euclidean metric). [ABSTRACT FROM AUTHOR]