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Nondegenerate Groups of Regular Points

  • 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

The defining property of an ORV-function f is that \(f\in \mathbb {{F}}_{+}\) is measurable and the upper limit function exists and is positive and finite (see Definition 3.7). The main aim of this chapter is to study a subclass of functions in ORV with “nondegenerate group of regular points”, that is, those ORV-functions for which a limit function exists (see Definition 3.2) and is positive and finite belonging to a certain multiplicative subgroup in R+.

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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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