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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Finitely additive Gleason measures


Author: Anatolij Dvurečenskij
Journal: Proc. Amer. Math. Soc. 115 (1992), 191-198
MSC: Primary 81P10; Secondary 03G12, 28A60, 46L50
MathSciNet review: 1072335
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Abstract: We describe the set of all finitely additive measures which attain also infinite values on a quantum logic of a Hilbert space and which are expressible via the generalized Gleason-Lugovaja-Sherstnev formula. We prove that this set consists of those which are regular with respect to the set of all finite-dimensional subspaces. In addition, we show that this regularity does not entail the countable additivity, in general.


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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1992-1072335-9
PII: S 0002-9939(1992)1072335-9
Keywords: Hilbert space, quantum logic, measure, Gleason measure, regular measure, bilinear form
Article copyright: © Copyright 1992 American Mathematical Society