On measurable solutions of a functional equation and its application to information theory
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 is given.
Belis and Guiasu studied a generalization of Shannon entropy as weighted or useful entropy. In this paper, the weighted entropy of type is defined and characterized and some if its properties are studied. Further generalizations involving more parameters of weighted entropy are also specified.
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