Extension and Application of Deleting Items and Disturbing Mesh Theorem of Riemann Integral

Abstract: The deleting items and disturbing mesh theorems of Riemann Integral are extended to multiple integral,line integral and surface integral respectively by constructing various of incomplete Riemann sum and non-Riemann sum sequences which converge to the same limit of classical Riemann sum. And, the deleting items and disturbing mesh formulae of Green's theorem, Stokes' theorem and divergence theorem (Gauss's or Ostrogradsky 's theorem) are also deduced. Then, the deleting items and disturbing mesh theorems of general Stokes' theorem on differential manifold are also derived.