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The deleting items and disturbing mesh theorems of Riemann Integral areextended to multiple integral,line integral and surface integral respectivelyby constructing various of incomplete Riemann sum and non-Riemann sum sequenceswhich converge to the same limit of classical Riemann sum. And, the deletingitems and disturbing mesh formulae of Green's theorem, Stokes' theorem anddivergence theorem (Gauss's or Ostrogradsky 's theorem) are also deduced. Then,the deleting items and disturbing mesh theorems of general Stokes' theorem ondifferential manifold are also derived.

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