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Characterization of a quantitative-qualitative measure of relative information. (English) Zbl 0558.94003

Using utilities [M. Belis and S. Guiaşu, IEEE Trans. Inf. Theory IT-14, 593-594 (1968)] the authors introduce and characterize a ”useful” self-information gain and a ”useful” directed divergence. Their characterization theorem is analogous to the Theorem in the paper mentioned above.
Reviewer: W.Sander

MSC:

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

[1] Aczel, J., (Lectures on Functional Equations and Their Applications (1966), Academic: Academic New York) · Zbl 0139.09301
[2] Kullback, S., Information Theory and Statistics (1959), Wiley: Wiley New York · Zbl 0149.37901
[3] Longo, G., Quantitative-Qualitative Measure of Information (1972), Springer: Springer New York
[4] Renyi, A., On measures of entropy and information, (Proceedings of the Fourth Berkeley Symposium on Mathematical Statistics and Probability, Univ. of California Press (1961)), 547-561
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