The Stokes Theorem for the Generalized Riemann Integral

Abstract

In $\mathbb{R}^m$, we define the generalized Riemann integral over normal $m$-dimensional currents with compact support and bounded multiplicities, and prove the Stokes theorem for continuous $(m-1)$-forms that are pointwise Lipschitz outside sets of $\sigma$-finite $(m-1)$-dimensional Hausdorff measure. In addition, we show that the usual transformation formula holds for local lipeomorphisms, which need not be injective