A remark on distributions and the de Rham theorem
  We show that the de Rham theorem, interpreted as the isomorphism between distributional de Rham cohomology and simplicial homology in the dual dimension for a simplicial decomposition of a compact oriented manifold, is a straightforward consequence of elementary properties of currents. The explicit construction of this isomorphism extends to other cases, such as relative and absolute cohomology spaces of manifolds with corners. 
Richard B. Melrose
math.DG