Mathematical Notes

, Volume 93, Issue 1–2, pp 217–223

Luzin’s correction theorem and the coefficients of Fourier expansions in the Faber-Schauder system

Article

Abstract

Suppose that bn ↓ 0 and Σn=1(bn/n)=+∞. In this paper, it is proved that any measurable almost everywhere finite function on [0, 1] can be corrected on a set of arbitrarily small measure to a continuous function \(\tilde f\) so that the nonzero moduli \(|A_n (\tilde f)|\) of the Fourier-Faber-Schauder coefficients of the corrected function are bn.

Keywords

Luzin’s correction theorem Faber-Schauder system correcting function Faber-Schauder spectrum 

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Copyright information

© Pleiades Publishing, Ltd. 2013

Authors and Affiliations

  1. 1.Yerevan State UniversityYerevanArmenia
  2. 2.Belorussian State UniversityBelorussianRussia

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