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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

States on quantum logics and their connection with a theorem of Alexandroff


Authors: O. R. Béaver and T. A. Cook
Journal: Proc. Amer. Math. Soc. 67 (1977), 133-134
MSC: Primary 81.06
MathSciNet review: 0452199
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Abstract: We generalize the notion of regularity of measures to quantum logics and then prove that each regular finitely additive state on a quantum logic is countably additive. Examples are given from measure theory and quantum mechanics.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0452199-6
PII: S 0002-9939(1977)0452199-6
Keywords: Quantum logics, states, regular measures
Article copyright: © Copyright 1977 American Mathematical Society