Regularity and 𝜎-additivity of states on quantum logics

Navara, Mirko

doi:10.1090/S0002-9939-1992-1079705-3

Regularity and $\sigma$-additivity of states on quantum logics
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Proc. Amer. Math. Soc. 115 (1992), 427-429 Request permission

Abstract:

In 1977, Béaver and Cook [1] introduced the notion of regularity of states on quantum logics. They presented a generalization of Alexandroff theorem: each regular finitely additive state on a quantum logic is countably additive. Recently, Dvurečenskij, Neubrunn, and Pulmannová [2] observed an incorrectness in the original proof and doubted thus the validity of the result. We construct here a counterexample.

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