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Keywords:
regular code; dyadic expansion; entropy
regular code; dyadic expansion; entropy
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 $\frak W$.
References:
[1] Katětov M.: On entropy-like functionals and codes for metrized probability spaces I. Comment. Math. Univ. Carolinae 31 (1990), 49-66. MR 1056171
[2] Katětov M.: Extended Shannon entropies. Czechoslovak Math. J. 33 (108) (1983), 546-601. MR 0721088
[3] Kolgomorov A.: On some asymptotic characteristics of totally bounded spaces (in Russian). Doklady Akad. Nauk SSSR 108 (1956), 385-389.
[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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