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A characterization of entropies of degree alpha. (English) Zbl 0469.94005


MSC:

94A17 Measures of information, entropy
39B99 Functional equations and inequalities
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References:

[1] Aczél, J., andZ. Daróczy: Characterisierung der Entropien positiver Ordnung und der Shannonschen Entropie. Acta Math. Acad. Sci. Hung.14, 1963, 95–121. · Zbl 0138.14904
[2] Behara, M., andP. Nath: Additive and Non-additive Entropies of Finite measurable partitions. Probability and Information Theory II. Lecture Notes in Math. Vol. 296. Berlin-Heidelberg-New York 1973, 102–138. · Zbl 0282.94020
[3] Chaundy, T.W., andJ.B. McLeod: On a Functional Equation. Edinburgh Math. Notes43, 1960, 7–8. · Zbl 0100.32703
[4] Daróczy, Z.: On the Measurable Solutions of a Functional Equation. Acta Math. Acad. Sci. Hung.22, 1971, 11–14. · Zbl 0236.39008
[5] Daróczy, Z., andA. Járai: On the Measurable Solution of a Functional Equation of the Information Theory. Acta Math. Acad. Sci. Hung.34, 1979, 105–116. · Zbl 0424.39002
[6] Daróczy, Z., andL. Losonczi: Über die Erweiterung der auf einer Punktmenge additiven Funktionen. Publ. Math. Debrecen14, 1967, 239–245. · Zbl 0175.15305
[7] Járai, A.: On Measurable Solutions of Functional Equations. Publ. Math. Debrecen26, 1979, 17–35.
[8] Kannappan, Pl.: On a Generalization of Some Measures in Information Theory. Glasnik Mat.9 (29), 1974, 81–93. · Zbl 0287.39006
[9] Mittal, D.P.: On Continuous Solutions of a Functional Equation. Metrika22, 1976, 31–40. · Zbl 0333.39006
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