I am looking for a generalized version of the Gauss-Green theorem also known as the divergence theorem:

http://en.wikipedia.org/wiki/Divergence_theorem

A quick search on MathSciNet suggests that there are generalizations for bad domains and nonsmooth functions. However, they seem to rely on heavy machinery and not to be suited for the special case I am interested in.

For example, I found this formula on PlanetMath:$$ \int_E \mathrm{div} f(x)\, dx = \int_{\partial^* E} \langle \nu_E(x),f(x)\rangle \,d\mathcal H^{n-1}(x)$$

See http://planetmath.org/?method=l2h&from=objects&name=GaussGreenTheorem&op=getobj for the details.

Let $\Omega \subset \mathbb{R}^n$ be open and bounded and $f\in C^1(\Omega, \mathbb{R}^n) \cap C^0(\overline\Omega, \mathbb{R}^n)$.

Question: What conditions do we have to impose on $\Omega$ (or $f$) to ensure that the divergence theorem holds true?