It can be seen from the above formulae that the limiting density function $\mathscr{V}_{\infty}=\frac{d\underline{\nu}_{\infty}}{dv}$ is a Lipschitz function on $\mathbb{I}$ and it is smooth everywhere in the interior of $\mathbb{I}$ except at $v=0$. On the other hand, the singular fiber of $\mathcal{F}$ precisely appears at $t=0$. So in our context, the singularity of the renormalized limit measure $d\underline{\nu}_{\infty}$ effectively characterizes the singularity behavior of the collapsing geometry.