Regular states and countable additivity on quantum logics

Dvurečenskij, Anatolij; Neubrunn, Tibor; Pulmannová, Sylvia

doi:10.1090/S0002-9939-1992-1045591-0

Regular states and countable additivity on quantum logics
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by Anatolij Dvurečenskij, Tibor Neubrunn and Sylvia Pulmannová PDF

Proc. Amer. Math. Soc. 114 (1992), 931-938 Request permission

Abstract:

We give a counterexample of the result of Béaver and Cook concerning a generalization of the Alexandroff theorem for regular, finitely-additive states on quantum logics using states on the system of all splitting subspaces of an incomplete inner-product space. Moreover, we introduce another type of state regularity which entails countable additivity of states on logics.

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