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Measurable solutions of functional equations related to information theory. (English) Zbl 0262.94019


MSC:

94A15 Information theory (general)
39B99 Functional equations and inequalities
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References:

[1] J. Aczél and Z. Daróczy, On measures of information and their characterizations, Academic Press [Harcourt Brace Jovanovich, Publishers], New York-London, 1975. Mathematics in Science and Engineering, Vol. 115. · Zbl 0345.94022
[2] Rudolf Borges, Zur Herleitung der Shannonschen Information, Math. Z. 96 (1967), 282 – 287 (German). · Zbl 0143.41301 · doi:10.1007/BF01123655
[3] Zoltán Daróczy, On the Shannon measure of information, Magyar Tud. Akad. Mat. Fiz. Oszt. Közl. 19 (1970), 9 – 24 (Hungarian, with German summary).
[4] Z. Daróczy and I. Kátai, Additive zahlentheoretische Funktionen und das Mass der Information, Ann. Univ. Sci. Budapest. Eötvös Sect. Math. 13 (1970), 83 – 88 (1971) (German). · Zbl 0216.32101
[5] Edwin Hewitt and Karl Stromberg, Real and abstract analysis, Springer-Verlag, New York-Heidelberg, 1975. A modern treatment of the theory of functions of a real variable; Third printing; Graduate Texts in Mathematics, No. 25. · Zbl 0307.28001
[6] P. L. Kannappan and P. N. Rathie, On a characterization of directed divergence, Information and Control 22 (1973), 163 – 171. · Zbl 0255.94011
[7] David G. Kendall, Functional equations in information theory, Z. Wahrscheinlichkeitstheorie und Verw. Gebiete 2 (1964), 225 – 229 (1964). · Zbl 0227.94009 · doi:10.1007/BF00533380
[8] P. M. Lee, On the axioms of information theory, Ann. Math. Statist. 35 (1964), 415 – 418. · Zbl 0124.11307 · doi:10.1214/aoms/1177703765
[9] P. N. Rathie and Pl. Kannappan, On a characterization of inaccuracy (submitted). · Zbl 0442.94003
[10] P. N. Rathie and Pl. Kannappan, On a functional equation connected with Shannon’s entropy, Funkcial. Ekvac. 14 (1971), 153 – 159. · Zbl 0237.39007
[11] Helge Tverberg, A new derivation of the information function, Math. Scand. 6 (1958), 297 – 298. · Zbl 0089.13401 · doi:10.7146/math.scand.a-10555
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