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Can anyone indicates a book with a quite complete proof of the Lebesgue differentiation of Lebesgue.

Th: Every function with bounded variation ( monotone) is differentiable almost everywhere.

Feel free to put a proof or parts of it, but it is not necessary.

I am having some trouble for understand the proof found in the book: Real Analysis by Stein /Shakarchi.

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    This is in most books on measure theory: there's a proof in Royden's book, for example, and Folland has a version (it's somewhat hard to recognize). Online, Terry Tao [has notes on it for a course of his](http://terrytao.wordpress.com/2010/10/16/245a-notes-5-differentiation-theorems/) (the approach there seems different from proofs using the Vitali lemma). You could also try asking about the proof in Stein-Shakarchi on this site.2012-02-23
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    Zygmund & Wheeden Measure and Integral. Personally, I realized that theorem but with some previous troubles understanding the Vitali's Lemmas.2012-02-23

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