Finitely additive Gleason measures

Dvurečenskij, Anatolij

doi:10.1090/S0002-9939-1992-1072335-9

Finitely additive Gleason measures
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by Anatolij Dvurečenskij

Proc. Amer. Math. Soc. 115 (1992), 191-198

DOI: https://doi.org/10.1090/S0002-9939-1992-1072335-9

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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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