Geodesic
On measurable solutions of a functional equation and their application to information theory
Applications of Mathematics, Tome 28 (1983) no. 2, pp. 103-107
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In this paper, measurable solutions of a functional equation with four unknown functions are obtained. As an application of the measurable solutions a joint characterization of Shannon's entropy and entropy of type $\beta$ is given.
In this paper, measurable solutions of a functional equation with four unknown functions are obtained. As an application of the measurable solutions a joint characterization of Shannon's entropy and entropy of type $\beta$ is given.
DOI : 10.21136/AM.1983.104010
Classification : 39B30, 39B99, 94A15, 94A17
Keywords: measurable solutions; system; Shannon’s entropy 
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Dial, Gur. On measurable solutions of a functional equation and their application to information theory. Applications of Mathematics, Tome 28 (1983) no. 2, pp. 103-107. doi: 10.21136/AM.1983.104010

[1] J. Aczel: Lectures on functional equations and their applications. Academic Press, New York, 1966. | MR | Zbl

[2] J. Aczel Z. Daroczy: On measures of information and their characterizations. Academic Press, New York, 1975. | MR

[3] Z. Daroczy, Losonczi: Über die Erweiterung der auf einer Punktmenge additive Funktion. Publ Math. Debrecen, 14 (1967) 239-245. | MR

[4] I. J. Taneja: A joint characterization of Shannons entropy of type through a functional equation. Journal of Mathematical Sciences, (10, 1975), 69-74. | MR

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