The Stokes theorem for the generalized Riemann integral. (English) Zbl 1023.26010

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.


26B20 Integral formulas of real functions of several variables (Stokes, Gauss, Green, etc.)