Abstract
We prove that, for every ε ∈ (0, 1), there is a measurable set E ⊂ [0, 1] whose measure |E| satisfies the estimate |E| > 1−ε and, for every function f ∈ C[0,1], there is ˜ f ∈ C[0,1] coinciding with f on E whose expansion in the Faber–Schauder system diverges in measure after a rearrangement.
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Original Russian Text © 2018 Grigoryan M.G. and Sargsyan A.A.
Yerevan. Translated from Sibirskii Matematicheskii Zhurnal, vol. 59, no. 5, pp. 1057–1065, September–October, 2018; DOI: 10.17377/smzh.2018.59.508.
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Grigoryan, M.G., Sargsyan, A.A. The Fourier–Faber–Schauder Series Unconditionally Divergent in Measure. Sib Math J 59, 835–842 (2018). https://doi.org/10.1134/S0037446618050087
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DOI: https://doi.org/10.1134/S0037446618050087