Abstract: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.
Keywords: orthomodular lattice, subadditive probability measure
AMS Subject Classification: Primary 06C15; Secondary 28E15, 81P10