Abstract
In this chapter we study the classical problem of the change of variables in the integral from a new viewpoint. We will compute how the Lebesgue measure in ℝn changes under a sufficiently regular transformation, generalizing what we have already seen for linear, or affine, maps. As a byproduct we obtain a quite general change of variables formula for integrals with respect to the Lebesgue measure.
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© 2011 Scuola Normale Superiore Pisa
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Ambrosio, L., Da Prato, G., Mennucci, A. (2011). Measurable transformations. In: Introduction to Measure Theory and Integration. Appunti/Lecture Notes, vol 10. Edizioni della Normale. https://doi.org/10.1007/978-88-7642-386-4_8
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DOI: https://doi.org/10.1007/978-88-7642-386-4_8
Publisher Name: Edizioni della Normale
Print ISBN: 978-88-7642-385-7
Online ISBN: 978-88-7642-386-4
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