I am referring to the page 260 of the book "Sets of finite perimeter and geometric measure theory" of F.Maggi:
Let $E$ be a set of locally finite perimeter and $H$ an open half space. At some point the book claims
$$ \int_{\partial^{\star}(E\setminus H)} \nu_{E\setminus H}dH^{n-1}=0$$ where $\nu$ is the measure theoretic outer normal. The book says that it holds due to the fact that if $E$ is a set of locally finite perimeter, then $\nu$ satisfies
$$ \nu_E(x)=\lim_{r\to 0} \frac{1}{\omega_{n-1}r^{n-1}}\int_{B_r(x)\cap\partial^{\star}E}\nu_EdH^{n-1}, \text{whenever}\ x\in\partial^{\star}E. $$
I am not seeing why and i think i need some help in order to understand
Thanks to anyone who will help me.