I'm reading [these notes](http://www.mat.univie.ac.at/~stein/lehre/SoSem09/distrvo.pdf), and there's a part I don't understand on page 72 (76 in the PDF), right after the equation marked with two stars.

> 
> Note that $\sqrt{1+|Dg(y')|^2}dy'$ is the surface measure $\mathrm{d}S$ of $M$ corresponding to the parametrisation $y'\mapsto(g(y'),y')$ of $M$
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A reference is then given, but I can only find it in German and can't understand it.

$y'$ is some point in $\mathbb{R}^{n-1}$, $M$ is a hypersurface in an open subset of $\mathbb{R}^n$. $g$ is a function from $\mathbb{R}^{n-1}$ to $\mathbb{R}$.