Regular states and countable additivity on quantum logics
Anatolij Dvurečenskij, Tibor Neubrunn, Sylvia Pulmannová · Proceedings of the American Mathematical Society · 1992
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.