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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:
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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