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
Full-text PDF Free Access
Similar Articles |
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)
Retrieve articles in Proceedings of the American Mathematical Society
Retrieve articles in all journals
© Copyright 1977 American Mathematical Society