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d'Andrea, A. B. ; de Lucia, P. ; Wright, J. D. Maitland
On Kalmbach measurability. (English). Applications of Mathematics, vol. 39 (1994), issue 6, pp. 445-447
MSC: 06C15, 28A60 | MR 1298732 | Zbl 0815.28004 | DOI: 10.21136/AM.1994.134270
Keywords:
Kalmbach measurability; Boolean algebra; orthomodular lattice
Summary:
In this note we show that, for an arbitrary orthomodular lattice $L$, when $\mu $ is a faithful, finite-valued outer measure on $L$, then the Kalmbach measurable elements of $L$ form a Boolean subalgebra of the centre of $L$.
References:
[1] E. Beltrametti, G. Cassinelli: The logic of quantum mechanics. Addison Wesley, Reading MA, 1981. MR 0635780
[2] L. Beran: Orthomodular Lattices. Algebraic approach, Academia, Prague and Reidel, Dordrecht, 1984. MR 0785005
[3] S. Gudder: Stochastic methods in quantum mechanics. North-Holland, Amsterdam, 1979. MR 0543489 | Zbl 0439.46047
[4] G. Kalmbach: Orthomodular lattices. Academic Press, London, 1983. MR 0716496 | Zbl 0528.06012
[5] G. Kalmbach: Quantum measure spaces. Foundations of Phys. 20 (1990), 801–821. DOI 10.1007/BF01889692 | MR 1067216
[6] P. Pták, S. Pulmannova: Orthomodular structures as quantum logics. Kluwer, Dordrecht, 1991. MR 1176314
[7] V. S. Varadarajan: Geometry of quantum theory. Springer-Verlag, Berlin, 1985. MR 0805158 | Zbl 0581.46061
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