Almost Everywhere Convergence of Greedy Algorithm with Respect to Vilenkin System

  • M. G. Grigoryan
  • S. A. Sargsyan
Real and Complex Analysis


In this paper, we prove that for any ε ∈ (0, 1) there exists ameasurable set E ∈ [0, 1) with measure |E| > 1 − ε such that for any function fL1[0, 1), it is possible to construct a function \(\tilde f \in {L^1}[0,1]\) coinciding with f on E and satisfying \(\int_0^1 {|\tilde f(x) - f(x)|dx < \varepsilon } \), such that both the Fourier series and the greedy algorithm of \(\tilde f\) with respect to a bounded Vilenkin system are almost everywhere convergent on [0, 1).


Vilenkin system convergence Fourier series greedy algorithm 

MSC2010 numbers

42C10 42C20 


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Copyright information

© Allerton Press, Inc. 2018

Authors and Affiliations

  1. 1.Yerevan State UmiversityYerevanArmenia

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