Geodesic
A measure-theoretic characterization of Boolean algebras among orthomodular lattices
Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 1, pp. 205-208

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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.
Classification : 03G12, 06C15, 28E15, 81P10
Keywords: orthomodular lattice; subadditive probability measure 
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Pták, Pavel; Pulmannová, Sylvia. A measure-theoretic characterization of Boolean algebras  among orthomodular lattices. Commentationes Mathematicae Universitatis Carolinae, Tome 35 (1994) no. 1, pp. 205-208. http://geodesic.mathdoc.fr/item/CMUC_1994__35_1_a19/