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
DOI:
https://doi.org/10.1090/S0002-9939-1970-0259056-2
MathSciNet review:
0259056
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Abstract | References | Similar Articles | Additional Information
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.
- Stanley P. Gudder, Quantum probability spaces, Proc. Amer. Math. Soc. 21 (1969), 296–302. MR 243793, DOI https://doi.org/10.1090/S0002-9939-1969-0243793-1
- Patrick Suppes, The probabilistic argument for a non-classical logic of quantum mechanics, Philos. Sci. 33 (1966), 14–21. MR 215575, DOI https://doi.org/10.1086/288067 W. Sierpinski, Les ensembles boreliens abstraits, Ann. Soc. Polon. Math. 6 (1927), 50-53.
- Paul R. Halmos, Measure Theory, D. Van Nostrand Company, Inc., New York, N. Y., 1950. MR 0033869
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Additional Information
Keywords:
Quantum probability space,
abstract Borel sets,
topological space
Article copyright:
© Copyright 1970
American Mathematical Society