Abstract
This chapter develops results concerning the Riemann integration of functions defined in \(\mathbb {R}^n\). We address in detail the standard necessary and sufficient condition of zero Lebesgue measure for the set of discontinuities for the Riemann integrability of a scalar function defined in \(\mathbb {R}^n\). Other topics such as change of variables are also presented in detail.
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Botelho, F.S. (2018). Integration in \(\mathbb {R}^n\) . In: Real Analysis and Applications. Springer, Cham. https://doi.org/10.1007/978-3-319-78631-5_9
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DOI: https://doi.org/10.1007/978-3-319-78631-5_9
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Publisher Name: Springer, Cham
Print ISBN: 978-3-319-78630-8
Online ISBN: 978-3-319-78631-5
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