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A note on quantum probability spaces

Author: Tibor Neubrunn
Journal: Proc. Amer. Math. Soc. 25 (1970), 672-675
MSC: Primary 28.10; Secondary 81.00
MathSciNet review: 0259056
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Abstract: In general the collection of sets closed with respect to countable disjoint unions and with respect to the complementation, generated by a given collection $ A$ does not coincide with the $ \sigma $-field generated by $ A$. In the present paper two necessary and sufficient conditions for the equality of the last mentioned systems are given. The coincidence of the above systems in cases when $ A$ is the collection of all open sets in a topological space is obtained as a corollary.

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

  • [1] S. P. Gudder, Quantum probability spaces, Proc. Amer. Math. Soc. 21 (1969), 296-302. MR 0243793 (39:5114)
  • [2] P. Suppes, The probabilistic argument for a non-classical logic of quantum mechanics, Philos. Sci. 33 (1966), 14-21. MR 35 #6415. MR 0215575 (35:6415)
  • [3] W. Sierpinski, Les ensembles boreliens abstraits, Ann. Soc. Polon. Math. 6 (1927), 50-53.
  • [4] P. R. Halmos, Measure theory, Van Nostrand, Princeton, N. J., 1950. MR 11, 504. MR 0033869 (11:504d)

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Keywords: Quantum probability space, abstract Borel sets, topological space
Article copyright: © Copyright 1970 American Mathematical Society

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