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
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