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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 $\frak W$.
[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