Remote Access Proceedings of the American Mathematical Society
Green Open Access

Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)



Regularity and $ \sigma$-additivity of states on quantum logics

Author: Mirko Navara
Journal: Proc. Amer. Math. Soc. 115 (1992), 427-429
MSC: Primary 03G12; Secondary 81P10
MathSciNet review: 1079705
Full-text PDF

Abstract | References | Similar Articles | Additional Information

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.

References [Enhancements On Off] (What's this?)

Similar Articles

Retrieve articles in Proceedings of the American Mathematical Society with MSC: 03G12, 81P10

Retrieve articles in all journals with MSC: 03G12, 81P10

Additional Information

Keywords: Quantum logic, regular states, countable additivity
Article copyright: © Copyright 1992 American Mathematical Society

American Mathematical Society