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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

ISSN 1088-6826 (online) ISSN 0002-9939 (print)

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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States on quantum logics and their connection with a theorem of Alexandroff
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by O. R. Béaver and T. A. Cook PDF
Proc. Amer. Math. Soc. 67 (1977), 133-134 Request permission

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.
References
  • Thurlow A. Cook, The geometry of generalized quantum logics, Internat. J. Theoret. Phys. 17 (1978), no. 12, 941–955. MR 552537, DOI 10.1007/BF00678422
    • N. Dunford and J. Schwartz, Linear operators. I, Interscience, New York, 1957.
  • Josef M. Jauch, Foundations of quantum mechanics, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1968. MR 0218062
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Additional Information
  • © Copyright 1977 American Mathematical Society
  • Journal: Proc. Amer. Math. Soc. 67 (1977), 133-134
  • MSC: Primary 81.06
  • DOI: https://doi.org/10.1090/S0002-9939-1977-0452199-6
  • MathSciNet review: 0452199