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Group-valued measures on coarse-grained quantum logics
Czechoslovak Mathematical Journal, Tome 57 (2007) no. 2, pp. 737-746
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In it was shown that a (real) signed measure on a cyclic coarse-grained quantum logic can be extended, as a signed measure, over the entire power algebra. Later () this result was re-proved (and further improved on) and, moreover, the non-negative measures were shown to allow for extensions as non-negative measures. In both cases the proof technique used was the technique of linear algebra. In this paper we further generalize the results cited by extending group-valued measures on cyclic coarse-grained quantum logics (or non-negative group-valued measures for lattice-ordered groups). Obviously, the proof technique is entirely different from that of the preceding papers. In addition, we provide a new combinatorial argument for describing all atoms of cyclic coarse-grained quantum logics.
In it was shown that a (real) signed measure on a cyclic coarse-grained quantum logic can be extended, as a signed measure, over the entire power algebra. Later () this result was re-proved (and further improved on) and, moreover, the non-negative measures were shown to allow for extensions as non-negative measures. In both cases the proof technique used was the technique of linear algebra. In this paper we further generalize the results cited by extending group-valued measures on cyclic coarse-grained quantum logics (or non-negative group-valued measures for lattice-ordered groups). Obviously, the proof technique is entirely different from that of the preceding papers. In addition, we provide a new combinatorial argument for describing all atoms of cyclic coarse-grained quantum logics.
Classification : 03G12, 06C15, 28A55, 28A99, 28B10, 81P10
Keywords: coarse-grained quantum logic; group-valued measure; measure extension 
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de Simone, Anna; Pták, Pavel. Group-valued measures on coarse-grained quantum logics. Czechoslovak Mathematical Journal, Tome 57 (2007) no. 2, pp. 737-746. http://geodesic.mathdoc.fr/item/CMJ_2007_57_2_a15/

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