Differentiation and Integration

  • Sergei Ovchinnikov
Part of the Universitext book series (UTX)


In the first three sections of this chapter, we investigate differentiability properties of functions of bounded variation. We begin by introducing the upper and lower derivatives of a function defined on a closed bounded interval [a, b] in Sect. 4.1, where important properties of these derivatives are established (cf. Lemma 4.1). Functions of bounded variation are introduced and their properties are investigated in Sect. 4.2. The main result (Theorem 4.8) of Sect. 4.3 asserts that a function of a bounded variation on [a, b] is differentiable almost everywhere on this interval.


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Copyright information

© Springer Science+Business Media New York 2013

Authors and Affiliations

  • Sergei Ovchinnikov
    • 1
  1. 1.Department of MathematicsSan Francisco State UniversitySan FranciscoUSA

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