Correlation of a signal with an amplitude-distorted form of itself

In comparing a signal f(t) with its amplitude-distorted form g(f(t)) , where g(\cdot) is a monotonically increasing function of its argument, one is led to consider the correlation function \begin{equation} R(s) \triangleq \int_{-\infty}^{\infty} dtg (f(t))f(t-s). \end{equation} A rigorous proof is given of the inequality R(s) \leq R(O) . Generalizations are presented for the cases of finite domains and of signals defined in two-dimensional space.