The general solution of a functional equation arising in information theory (Q1088081)

The author gives all solutions of the functional equation \[ f(pq)+f(p(1- q))=f(p)(f(q)+f(1-q)) \] where p,q\(\in [0,1]\) and f is the unknown function f:[0,1]\(\to R\). The solutions are determined by showing that they can be expressed by the solution of the fundamental Cauchy equations \(f(xy)=f(x)f(y),\) x,y\(\in [0,1]\) and \(f(x+y)=f(x)+f(y),\) x,y\(\in R\).