I was wondering if Stokes' theorem could be formulated in a setting which could be easily applied in situations where the traditional form cannot, such as on manifolds with corners like a rectangle or on a cone. I was thinking of something like:
If $M$ is a n-dimensional oriented Lipschitz-manifold with boundary and $\omega$ a compactly supported locally Lipschitz $n-1$-form on $M$, then $\int_{M}d\omega=\int_{\partial M}\omega.$
The notion of the (exterior) derivative of a form would of course have to include some notion of almost everywhereness on $M$, like applying Rademacher's theorem to the functions $\omega\circ\phi$ for a countable cover with charts $\phi$. I wonder if this has been done or can be done at all.