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Karamata’s Theorem for Integrals

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

Abstract

In this chapter, we continue to study some functions with nondegenerate groups of regular points, namely the regularly log-periodic functions considered in Chap.  5. The main aim of this chapter is to extend the well-known Karamata theorem on the asymptotic behavior of integrals of RV-functions to the case of log-periodic functions. For this class of functions, we are able to obtain the precise asymptotic behavior of integrals similarly to the class RV and determine the limit values.

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Copyright information

© 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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