The Stokes theorem for the generalized Riemann integral
In this paper, the author defines in \({\mathbb R}^m\) a generalized Riemann integral over \(m\)-dimensional currents with compact support and bounded multiplicities. He then proves in this setting the Stokes theorem for continuous \((m-1)\)-forms that are pointwise Lipschitz outside sets of \(\sigma\)-finite \((m-1)\)-dimensional Hausdorff measure. For such an integral, the usual transformation formula is also proved for local lipeomorphisms, not necessarily injective.
scientific article; zbMATH DE number 1848865