Luzin’s correction theorem and the coefficients of Fourier expansions in the Faber-Schauder system
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- Grigoryan, M.G. & Krotov, V.G. Math Notes (2013) 93: 217. doi:10.1134/S0001434613010239
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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.