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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?

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    Yes i was aware of Kolmogorov complexity, and various such notions, but they are not defined for continuous functions (to the best of my knowledge, that is).2011-12-31

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