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Proceedings of the American Mathematical Society

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Regularity and $ \sigma$-additivity of states on quantum logics


Author: Mirko Navara
Journal: Proc. Amer. Math. Soc. 115 (1992), 427-429
MSC: Primary 03G12; Secondary 81P10
DOI: https://doi.org/10.1090/S0002-9939-1992-1079705-3
MathSciNet review: 1079705
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Abstract: In 1977, Béaver and Cook [1] introduced the notion of regularity of states on quantum logics. They presented a generalization of Alexandroff theorem: each regular finitely additive state on a quantum logic is countably additive. Recently, Dvurečenskij, Neubrunn, and Pulmannová [2] observed an incorrectness in the original proof and doubted thus the validity of the result. We construct here a counterexample.


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DOI: https://doi.org/10.1090/S0002-9939-1992-1079705-3
Keywords: Quantum logic, regular states, countable additivity
Article copyright: © Copyright 1992 American Mathematical Society