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Proceedings of the American Mathematical Society

Published by the American Mathematical Society since 1950, Proceedings of the American Mathematical Society is devoted to shorter research articles in all areas of pure and applied mathematics.

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

The 2020 MCQ for Proceedings of the American Mathematical Society is 0.85.

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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.

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