, Volume 93, Issue 1-2, pp 217-223
Date: 02 Mar 2013

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

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Abstract

Suppose that b n ↓ 0 and Σ n=1 (b n /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 b n .

Original Russian Text © M. G. Grigoryan, V. G. Krotov, 2013, published in Matematicheskie Zametki, 2013, Vol. 93, No. 2, pp. 172–178.