Quasiunconditional basis property of the Faber – Schauder system

• Date: 2019
• Main Authors: Grigoryan, M. G., Krotov, V. G., Григорян, М. Г., Кротов, В. Г.
• Format: Article
• Language: Russian
• Published: Institute of Mathematics, NAS of Ukraine 2019
• Online Access: https://umj.imath.kiev.ua/index.php/umj/article/view/1432
• Journal Title: Ukrains’kyi Matematychnyi Zhurnal

We prove that, for any $0 < \delta < 1$, there exists a measurable set $E_{\delta} \subset [0, 1], \mathrm{m}\mathrm{e}\mathrm{s} (E_{\delta }) > 1 \delta $, such that for any function $f \in C[0, 1]$, one can find a function $\widetilde f \in C[0, 1]$ that coincides with...