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Article

Pták, Pavel ; Pulmannová, Sylvia
A measure-theoretic characterization of Boolean algebras among orthomodular lattices. (English). Commentationes Mathematicae Universitatis Carolinae, vol. 35 (1994), issue 1, pp. 205-208
MSC: 03G12, 06C15, 28E15, 81P10 | MR 1292596 | Zbl 0805.06010
Keywords:
orthomodular lattice; subadditive probability measure
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.
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