Abstract
In this section we deal with changes of variable in R d and with their relation to Lebesgue measure. The main result is Theorem 6.1.6. Let us begin by recalling some definitions.
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Notes
The proof of Theorem 6.1.6 presented here was inspired by one given by A. M. Gleason in some unpublished notes on advanced calculus.
Munroc [64], Rudin [75], and Wheeden and Zygmund [87] carry the study of the differentiation of measures and functions a bit farther than it is taken here. See Bruckner [13], Bruckner [14], de Guzmán [37], Hayes and Pauc [40], Kölzow [51], and Saks [76] for more advanced treatments of differentiation theory.
The proof of Theorem 6.3.10 given here is taken from Walker [85].
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© 1980 Springer Science+Business Media New York
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Cohn, D.L. (1980). Differentiation. In: Measure Theory. Birkhäuser, Boston, MA. https://doi.org/10.1007/978-1-4899-0399-0_6
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DOI: https://doi.org/10.1007/978-1-4899-0399-0_6
Publisher Name: Birkhäuser, Boston, MA
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