this question comes from theoretical Physics, the issue being the so called Path Integral. The measure of this thing is something written as
$[d\phi]=\prod_x d\phi(x)$
And this should be the limit of something defined by working on a discrete lattice of points over the integration domain: this lattice becomes finer and finer and you get some formal definition of the above formula.
Now, the question. I assume that the following equation does NOT hold (by considering the above mentioned limiting procedure), where $a$ is just some constant number:
$[d(a\phi)]= a[d\phi]$
Correct? I imagine to get something that goes like $a^N$, where $N$ is the number of points in each finite lattice discretization.