On a Class of Functional Equations in Distribution

AbstractIn this article, we present the most general solution of the functional equationsf(xy)+f((1−x)(1−y))=f(x(1−y))+f(y(1−x)) andf(xy)+f(x(1−y))+f(y(1−x))+f((1−x)(1−y))=f(x)+f(1−x)+f(y)+f(1−y) in the domain of distributions; and show that for regular distributions the solutions are the same as the classical solutions. These functional equations arise in connection with the characterization of sum form information measures