Abstract
Classical information theory considers the Information \(\mathcal{I}\) on the lattice \((\mathfrak{P},\wedge ,\vee )\) of partitions.
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Notes
- 1.
Compare Definition 9.10.
- 2.
It is surprising that the “opposite” orderings ≤ and \(\preccurlyeq \) coincide on \(\mathfrak{P}\).
- 3.
Here our requirement added to Definition 9.1 leads to the requirement that \(p(\omega )\neq 0\) for every \(\omega \in \Omega \). So \(\mathfrak{P}\) only has a largest element, if Ω is countable.
References
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Palm, G. (2012). Information Theory on Lattices of Covers. In: Novelty, Information and Surprise. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-29075-6_17
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DOI: https://doi.org/10.1007/978-3-642-29075-6_17
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