Abstract
In quantum mechanics each observable of a physical system defines a mapping from the set of states of the system to the set of probability measures on the value space of the observable. This mapping is σ-convex (in all conceivable ways) and it has some natural continuity properties. The paper aims to investigate the properties of this mapping in detail. In that the usual Hilbert space formulation of quantum mechanics will be applied. The notations and terminology will be fixed next. In that we follow rather closely the monographs of Beltrametti and Cassinelli (1981) and of Davies (1976). On the basic results of the Hilbert space operator theory we rely on Reed and Simon (1971).
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References
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© 1993 Springer Science+Business Media Dordrecht
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Cassinelli, G., Lahti, P.J. (1993). Sigma-Convex Structures of The Sets of States and Probability Measures in Quantum Mechanics. In: Corsi, G., Chiara, M.L.D., Ghirardi, G.C. (eds) Bridging the Gap: Philosophy, Mathematics, and Physics. Boston Studies in the Philosophy of Science, vol 140. Springer, Dordrecht. https://doi.org/10.1007/978-94-011-2496-6_11
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DOI: https://doi.org/10.1007/978-94-011-2496-6_11
Publisher Name: Springer, Dordrecht
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