Dębowski Łukasz
Institute of Computer Science, Polish Academy of Sciences, ul. Jana Kazimierza 5, 01-248 Warszawa, Poland.
Entropy (Basel). 2020 Jan 9;22(1):79. doi: 10.3390/e22010079.
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.
我们给出了完备性不变性的修正证明以及任意场的香农信息测度的链式法则，正如德博夫斯基在2009年所阐述的那样。我们的修正证明基于一些关于香农信息测度的辅助近似结果，这些结果可能具有独立的研究价值。正如本文中也简要讨论的那样，场的香农信息测度的广义微积分，包括完备性不变性和链式法则，特别有助于研究平稳过程的遍历分解及其与自然语言统计建模的联系。
