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Conditional entropy and Rokhlin metric. (English) Zbl 0949.28015
The paper is devoted to the study of some properties of systems of atoms of fuzzy sub-\(\sigma \)-algebras (in the sense of Klement). For a given fuzzy probability space \((X,\mathcal M, m)\), a pseudometric on an \(m\)-equivalence class \([\mathcal N]\) of fuzzy sub-\(\sigma \)-algebras is introduced. Applying a specific \(m\)-based equivalence, the so-called Rokhlin metric on relevant equivalence classes of a given \(m\)-equivalence class \([\mathcal N]\) is constructed. Although the paper gives no examples and it has some notational inaccuracies, it is an interesting contribution with possible applications in the entropy and other information measures domain.

MSC:
28E10 Fuzzy measure theory
28D20 Entropy and other invariants
94A17 Measures of information, entropy
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