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Entropy on effect algebras with the Riesz decomposition property I: Basic properties
Kybernetika, Tome 41 (2005) no. 2, pp. 143-160 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

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We define the entropy, lower and upper entropy, and the conditional entropy of a dynamical system consisting of an effect algebra with the Riesz decomposition property, a state, and a transformation. Such effect algebras allow many refinements of two partitions. We present the basic properties of these entropies and these notions are illustrated by many examples. Entropy on MV-algebras is postponed to Part II.
We define the entropy, lower and upper entropy, and the conditional entropy of a dynamical system consisting of an effect algebra with the Riesz decomposition property, a state, and a transformation. Such effect algebras allow many refinements of two partitions. We present the basic properties of these entropies and these notions are illustrated by many examples. Entropy on MV-algebras is postponed to Part II.
Classification : 03B50, 03G12, 06D35, 28A20, 37B40
Keywords: effect algebra; Riesz decomposition property; MV-algebra; state; entropy 
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     title = {Entropy on effect algebras with the {Riesz} decomposition property {I:} {Basic} properties},
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Di Nola, Antonio; Dvurečenskij, Anatolij; Hyčko, Marek; Manara, Corrado. Entropy on effect algebras with the Riesz decomposition property I: Basic properties. Kybernetika, Tome 41 (2005) no. 2, pp. 143-160. http://geodesic.mathdoc.fr/item/KYB_2005_41_2_a3/

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