If $f:\mathbb{R}^{n} \rightarrow \mathbb{R}^{n}$ is $C^1$ class and $det f^{\prime}(0)=0$ show that, when $r\rightarrow 0$
$$\dfrac{Vol(f(B[0,r]))}{ Vol(B[0,r])} \rightarrow 0$$

where $Vol(X)$ is n-dimensional volume to set $J$-measurable $X$.

Any suggestions are welcome, thanks