Geodesic
Modular atomic effect algebras and the existence of subadditive states
Kybernetika, Tome 40 (2004) no. 4, pp. 459-468 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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Lattice effect algebras generalize orthomodular lattices and $MV$-algebras. We describe all complete modular atomic effect algebras. This allows us to prove the existence of ordercontinuous subadditive states (probabilities) on them. For the separable noncomplete ones we show that the existence of a faithful probability is equivalent to the condition that their MacNeille complete modular effect algebra.
Lattice effect algebras generalize orthomodular lattices and $MV$-algebras. We describe all complete modular atomic effect algebras. This allows us to prove the existence of ordercontinuous subadditive states (probabilities) on them. For the separable noncomplete ones we show that the existence of a faithful probability is equivalent to the condition that their MacNeille complete modular effect algebra.
Classification : 03G12, 06F99, 81P10
Keywords: effect algebra; modular atomic effect algebra; subadditive state; MacNeille completion of an effect algebra 
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     author = {Rie\v{c}anov\'a, Zdenka},
     title = {Modular atomic effect algebras and the existence of subadditive states},
     journal = {Kybernetika},
     pages = {459--468},
     year = {2004},
     volume = {40},
     number = {4},
     mrnumber = {2102364},
     zbl = {1249.03120},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2004_40_4_a3/}
}
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Riečanová, Zdenka. Modular atomic effect algebras and the existence of subadditive states. Kybernetika, Tome 40 (2004) no. 4, pp. 459-468. http://geodesic.mathdoc.fr/item/KYB_2004_40_4_a3/