In this paper, we develop an elementary proof of the change of variables inmultiple integrals. Our proof is based on an induction argument. Assuming theformula for (m-1)-integrals, we define the integral over hypersurface in Rm,establish the divergent theorem and then use the divergent theorem to prove theformula for m-integrals. In addition to its simplicity, an advantage of ourapproach is that it yields the Brouwer Fixed Point Theorem as a corollary.
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