For example, continuous functions from $\mathbb{R}$ to $\mathbb{R}$ with nth derivative = 0.
Each function acts like a point in an $\mathbb{R}^n$ dimensional space with its Taylor expansion coefficients acting as coordinates:
$y=1 \rightarrow (1,0,0,...,0)$
$y=1+x+2x^{n-1} \rightarrow (1,1,0,...,2)$
Then the measure of the set of functions is simply its hypervolume in $\mathbb{R}^n$, or the measure of some lower dimensional shape it makes.
Does this scheme correctly outline the idea of a formal measure space? If so, is there a name for it or a more general method? The same basic idea should work for all kinds of vector spaces of functions: fourier series, spherical harmonics, bessel functions, etc.
I'm motivated by a physics problem where I'm trying to determine the entropy of a system which is easier to model with continuous mass rather than discrete particles. Intuitively I just need to quantify the number of states available to the system, and defining a measure for the set of possible distributions seems to be the way to go.