On the change of variables formula for multiple integrals
Classical Analysis and ODEs
2017-05-17 v2
Abstract
In this paper, we develop an elementary proof of the change of variables in multiple integrals. Our proof is based on an induction argument. Assuming the formula for (m-1)-integrals, we define the integral over hypersurface in Rm, establish the divergent theorem and then use the divergent theorem to prove the formula for m-integrals. In addition to its simplicity, an advantage of our approach is that it yields the Brouwer Fixed Point Theorem as a corollary.
Cite
@article{arxiv.1603.08428,
title = {On the change of variables formula for multiple integrals},
author = {Shibo Liu and Yashan Zhang},
journal= {arXiv preprint arXiv:1603.08428},
year = {2017}
}
Comments
6 pages