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Piron's and Bell's Geometrical Lemmas

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Abstract

The famous Gleason's Theorem gives a characterization of measures on lattices of subspaces of Hilbert spaces. The attempts to simplify its proof lead to geometrical lemmas that possess also easy proofs of some consequences of Gleason's Theorem. We contribute to these results by solving two open problems formulated by Chevalier, Dvurečenskij and Svozil. Besides, our use of orthoideals provides a unified approach to finite and infinite measures.

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Authors and Affiliations

  1. Center for Machine Perception, Department of Cybernetics, Faculty of Electrical Engineering, Czech Technical University, Technická 2, 166 27 Praha, Czech Republic

    Mirko Navara

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  1. Mirko Navara
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Navara, M. Piron's and Bell's Geometrical Lemmas. International Journal of Theoretical Physics 43, 1587–1594 (2004). https://doi.org/10.1023/B:IJTP.0000048804.78491.34

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  • DOI: https://doi.org/10.1023/B:IJTP.0000048804.78491.34

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