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Open AccessArticle

Approximating Information Measures for Fields

Institute of Computer Science, Polish Academy of Sciences, ul. Jana Kazimierza 5, 01-248 Warszawa, Poland
Entropy 2020, 22(1), 79; https://doi.org/10.3390/e22010079
Received: 20 November 2019 / Revised: 6 January 2020 / Accepted: 8 January 2020 / Published: 9 January 2020
(This article belongs to the Special Issue Information Theory and Language)
We supply corrected proofs of the invariance of completion and the chain rule for the Shannon information measures of arbitrary fields, as stated by Dębowski in 2009. Our corrected proofs rest on a number of auxiliary approximation results for Shannon information measures, which may be of an independent interest. As also discussed briefly in this article, the generalized calculus of Shannon information measures for fields, including the invariance of completion and the chain rule, is useful in particular for studying the ergodic decomposition of stationary processes and its links with statistical modeling of natural language. View Full-Text
Keywords: Shannon information measures; fields; invariance of completion; chain rule Shannon information measures; fields; invariance of completion; chain rule
MDPI and ACS Style

Dębowski, Ł. Approximating Information Measures for Fields. Entropy 2020, 22, 79.

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