@Article{JMS-50-268,
author = {Liu , Shibo and Zhang , Yashan},
title = {On the Change of Variables Formula for Multiple Integrals},
journal = {Journal of Mathematical Study},
year = {2017},
volume = {50},
number = {3},
pages = {268--276},
abstract = {<p style="text-align: justify;">We develop an elementary proof of the change of variables formula 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 $\mathbb{R}^m$, 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.</p>},
issn = {2617-8702},
doi = {https://doi.org/10.4208/jms.v50n3.17.04},
url = {http://global-sci.org/intro/article_detail/jms/10620.html}
}