It states:
Let $g:A \to R^n$ be continuously differentiable, where $A \subset R^n$ is open, and let $B=${${x \in A: \det g'(x)=0}$}. Thne $g(B)$ has measure $0$.
Okay.... obviously this theorem is right... but why don't constant functions violate this? After all, the derivative of a constant function is $0$ EVERYWHERE.... so that can't possibly be measure zero!