In the Wikipedia article on Stokes' theorem the following claim is advanced without any references given:

The main challenge in a precise statement of Stokes' theorem is in defining the notion of a

boundary. Surfaces such as the Koch snowflake, for example, are well-known not to exhibit a Riemann-integrable boundary, and the notion of surface measure in Lebesgue theory cannot be defined for a non-Lipschitz surface. One (advanced) technique is to pass to a weak formulation and then apply the machinery of geometric measure theory; for that approach see the coarea formula.

Can someone explain what is the weak formulation announced here and how exactly can we obtain the general Stokes' theorem in $\mathbb{R}^{3}$ for surfaces with non-smooth boundaries?