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Measurable transformations

  • Luigi Ambrosio
  • Giuseppe Da Prato
  • Andrea Mennucci
Part of the Appunti/Lecture Notes book series (PSNS, volume 10)

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 ℝ n 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.

Keywords

Lebesgue Measure Variable Formula Jacobian Determinant Measurable Transformation Disjoint Ball 
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Copyright information

© Scuola Normale Superiore Pisa 2011

Authors and Affiliations

  • Luigi Ambrosio
    • 1
  • Giuseppe Da Prato
    • 1
  • Andrea Mennucci
    • 1
  1. 1.Scuola Normale SuperiorePisaItaly

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