• Sheldon Axler
Open Access
Part of the Graduate Texts in Mathematics book series (GTM, volume 282)


In this chapter we see how to answer this question by considering differentiation issues. We begin by developing a powerful tool called the Hardy–Littlewood maximal inequality. This tool is used to prove an almost everywhere version of the Fundamental Theorem of Calculus. These results lead us to an important theorem about the density of Lebesgue measurable sets.

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© Sheldon Axler 2020

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Authors and Affiliations

  • Sheldon Axler
    • 1
  1. 1.Department of MathematicsSan Francisco State UniversitySan FranciscoUSA

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