States on quantum logics and their connection with a theorem of Alexandroff
O. R. Béaver and T. A. Cook
Proc. Amer. Math. Soc. 67 (1977), 133-134
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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.
A. Cook, The geometry of generalized quantum logics, Internat.
J. Theoret. Phys. 17 (1978), no. 12, 941–955.
N. Dunford and J. Schwartz, Linear operators. I, Interscience, New York, 1957.
M. Jauch, Foundations of quantum mechanics, Addison-Wesley
Publishing Co., Reading, Mass.-London-Don Mills, Ont., 1968. MR 0218062
- T. A. Cook, The geometry of generalized quantum logics, Internat. J. Theoret. Phys. (to appear). MR 552537 (80k:81009)
- N. Dunford and J. Schwartz, Linear operators. I, Interscience, New York, 1957.
- J. M. Jauch, Foundations of quantum mechanics, Addison-Wesley, Reading, Mass., 1968. MR 0218062 (36:1151)
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