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On a class of functional equations in distribution. (English) Zbl 0914.39030
The most general solutions of the functional equations arising in connection with the characterization of sum form information measures, $$f(xy)+ f(x(1-y))+ f(y(1-x))+ f((1-x)(1-y))= f(x)+ f(1-x)+ f(y)+ f(1-y),$$ and $$f(xy)+ f((1-x)(1-y))= f(x(1-y))+ f(y(1-x)),$$ are obtained in the domain of distributions.

MSC:
39B52Functional equations for functions with more general domains and/or ranges
94A17Measures of information, entropy
46F10Operations with distributions (generalized functions)
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References:
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