OK so we have:

$\displaystyle \int f(z) e^{a g(z)} dz^3$

integerated over all space.

Now there is a identity for this integral as an average, or something like that, right? What is it? Or perhaps you have suggestions where I could read up on that kind of thing?

(I'm not looking for the integral in terms of a determinant by the way, or am I? :/ ).

Any help would be much appreciated. Thanks.