A measure-theoretic characterization of Boolean algebras among orthomodular lattices
Pavel Pták, Sylvia Pulmannová · Czech digital mathematics library · 1994
summary:We investigate subadditive measures on orthomodular lattices. We show as the main result that an orthomodular lattice has to be distributive (=Boolean) if it possesses a unital set of subadditive probability measures. This result may find an application in the foundation of quantum theories, mathematical logic, or elsewhere.