Given a function (functional actually) $f(x,g(x))$, can a notion of simplicity be attached with respect to the function $g(x)$? (all functions and args are real).
Specifically, intuitively one could say that the function $f(x,0)$ is simpler than the general function $f(x,g(x))$ - notice that $g(x)$ is null- because it eliminates terms. However, how could one quantify this using some measure of $f$? For example, energy arguments could be used. Is there a way to do this?