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Proceedings of the American Mathematical Society

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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.

References [Enhancements On Off] (What's this?)

  • [1] Thurlow A. Cook, The geometry of generalized quantum logics, Internat. J. Theoret. Phys. 17 (1978), no. 12, 941–955. MR 552537, 10.1007/BF00678422
  • [2] N. Dunford and J. Schwartz, Linear operators. I, Interscience, New York, 1957.
  • [3] Josef M. Jauch, Foundations of quantum mechanics, Addison-Wesley Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1968. MR 0218062

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Keywords: Quantum logics, states, regular measures
Article copyright: © Copyright 1977 American Mathematical Society