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.
KeywordsLebesgue Measure Variable Formula Jacobian Determinant Measurable Transformation Disjoint Ball
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