Properties of Absolutely Continuous Functions

  • Valeriĭ V. Buldygin
  • Karl-Heinz Indlekofer
  • Oleg I. Klesov
  • Josef G. Steinebach
Part of the Probability Theory and Stochastic Modelling book series (PTSM, volume 91)


Absolutely continuous functions are an important class of functions for both applications and theory. Every polynomial of a finite order as well as every differentiable function is absolutely continuous. Moreover, any solution of an ordinary differential equation is absolutely continuous, since the latter is at least one times differentiable. These examples are not exhaustive. In this chapter, we consider conditions under which absolutely continuous functions belong to the classes PRV, PI, SQI, or POV (see Definitions 3.16–3.32). The results obtained in this chapter will be used throughout the book, for example, in Chaps. 5–9.


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© Springer Nature Switzerland AG 2018

Authors and Affiliations

  • Valeriĭ V. Buldygin
    • 1
  • Karl-Heinz Indlekofer
    • 2
  • Oleg I. Klesov
    • 3
  • Josef G. Steinebach
    • 4
  1. 1.Department of Mathematical AnalysisNational Technical University of UkraineKyivUkraine
  2. 2.Department of MathematicsUniversity of PaderbornPaderbornGermany
  3. 3.Department of Mathematical Analysis and Probability TheoryNational Technical University of UkraineKyivUkraine
  4. 4.Mathematical InstituteUniversity of CologneCologneGermany

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