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Extended Shannon entropies. II. (English) Zbl 0601.94004
Extended Shannon entropies $$C_{\tau}$$ and semientropies $$C^*_{\tau}$$, introduced in Part I [ibid. 33(108), 564-601 (1983; Zbl 0542.94007)] are examined. It is shown that $$C_{\tau}(P)$$ and $$C^*_{\tau}(P)$$ are finite whenever P satisfies a certain boundedness condition and that, under some not too restrictive assumptions, $$C_{\tau}$$ and $$C^*_{\tau}$$ satisfy a condition of the Lipschitz type.
##### MSC:
 94A17 Measures of information, entropy
semientropies
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##### References:
 [1] W. W. Comfort S. Negrepontis: The theory of ultrafilters. Springer-Verlag, New York–Heidelberg, 1974. · Zbl 0298.02004 [2] N. Dinculeanu: Vector measures. Berlin, 1966. · Zbl 0142.10502 [3] M. Katětov: Quasi-entropy of finite weighted metric spaces. Comment. Math. Univ. Carolinae 17 (1976), 777-806. · Zbl 0351.94013 · eudml:16795 [4] M. Katětov: Extensions of the Shannon entropy to semimetrized measure spaces. Comment. Math. Univ. Carolinae 21 (1980), 171-192. · Zbl 0445.94007 · eudml:17025 [5] M. Katětov: Extended Shannon entropies I. Czechosl. Math. J. 33 (108) (1983), 564-601. · Zbl 0542.94007 · eudml:13417 [6] E. Marczewski R. Sikorski: Measures in non-separable metric spaces. Colloq. Math 1 (1948), 133-139. · Zbl 0037.32201 · eudml:209895
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