Luzin’s correction theorem and the coefficients of Fourier expansions in the Faber-Schauder system
Martin Gevorgovich Grigoryan, В. Г. Кротов · Mathematical Notes · 2013
Suppose that b n ↓ 0 and Σ =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 .