On a class of functional equations in distribution (Q1269609)

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.