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Dial, Gur
On measurable solutions of a functional equation and their application to information theory. (English). Aplikace matematiky, vol. 28 (1983), issue 2, pp. 103-107
MSC: 39B30, 39B99, 94A15, 94A17 | MR 0695183 | Zbl 0513.39006 | DOI: 10.21136/AM.1983.104010
Keywords:
measurable solutions; system; Shannon’s entropy
Summary:
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.
References:
[1] J. Aczel: Lectures on functional equations and their applications. Academic Press, New York, 1966. MR 0208210 | Zbl 0139.09301
[2] J. Aczel Z. Daroczy: On measures of information and their characterizations. Academic Press, New York, 1975. MR 0689178
[3] Z. Daroczy, Losonczi: Über die Erweiterung der auf einer Punktmenge additive Funktion. Publ Math. Debrecen, 14 (1967) 239-245. MR 0240492
[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 0539497
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