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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



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.

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