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][1] 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.

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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?

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To clarify my question: I know that requiring the boundary of $\Omega$ to be piecewise regular is sufficient for the Gauss-Green theorem to be true. I wondered if this condition is also necessary. If so: is the an other "version" of Gauss-Green (e.g. the one cited above) which holds true under weaker conditions and is especially suited for the case of an open and bounded domain


  [1]: http://www.ams.org/mathscinet/search/publications.html?pg5=TI&s5=gauss+green