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.

  • 2
    $\begingroup$ 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 (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. $\endgroup$ – Dylan Moreland Feb 23 '12 at 3:09
  • $\begingroup$ Zygmund & Wheeden Measure and Integral. Personally, I realized that theorem but with some previous troubles understanding the Vitali's Lemmas. $\endgroup$ – leo Feb 23 '12 at 20:09

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