Real Analysis: Measure Theory, Integration, and Hilbert Spaces
by Elias M. Stein, Rami Shakarchi · Princeton University Press
Volume III of the Princeton Lectures in Analysis; chapter 3 develops differentiation of the integral through the Vitali covering lemma, the Hardy-Littlewood maximal function, its weak-type bound, and the Lebesgue differentiation theorem, with exercises and problems.
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Wolfram MathWorld
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