# Article

 Title: On entropy-like functionals and codes for metrized probability spaces II (English) Author: Katětov, Miroslav Language: English Journal: Commentationes Mathematicae Universitatis Carolinae ISSN: 0010-2628 (print) ISSN: 1213-7243 (online) Volume: 33 Issue: 1 Year: 1992 Pages: 79-95 . Category: math . Summary: In Part I, we have proved characterization theorems for entropy-like functionals $\delta$, $\lambda$, $E$, $\Delta$ and $\Lambda$ restricted to the class consisting of all finite spaces $P\in \frak W$, the class of all semimetric spaces equipped with a bounded measure. These theorems are now extended to the case of $\delta$, $\lambda$ and $E$ defined on the whole of $\frak W$, and of $\Delta$ and $\Lambda$ restricted to a certain fairly wide subclass of $\frak W$. (English) Keyword: regular code Keyword: dyadic expansion Keyword: entropy MSC: 54E35 MSC: 94A17 idZBL: Zbl 0751.94004 idMR: MR1173750 . Date available: 2009-01-08T17:53:48Z Last updated: 2012-04-30 Stable URL: http://hdl.handle.net/10338.dmlcz/118474 . Reference: [1] Katětov M.: On entropy-like functionals and codes for metrized probability spaces I.Comment. Math. Univ. Carolinae 31 (1990), 49-66. MR 1056171 Reference: [2] Katětov M.: Extended Shannon entropies.Czechoslovak Math. J. 33 (108) (1983), 546-601. MR 0721088 Reference: [3] Kolgomorov A.: On some asymptotic characteristics of totally bounded spaces (in Russian).Doklady Akad. Nauk SSSR 108 (1956), 385-389. Reference: [4] Kolgomorov A., Tihomirov V.: $\varepsilon$-entropy and $\varepsilon$-capacity of sets in function spaces (in Russian).Uspehi Mat. Nauk 14 no. 2 (1959), 3-86. MR 0112032 .

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