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For any countable set $D \subset [0,1]$, we construct a bounded measurable function $f$ such that the Fourier series of $f$ with respect to the regular general Haar system is divergent on $D$ and convergent on $[0,1]\backslash D$.
In this paper we proved that the Faber--Schauder functions form an unconditional representation system for $L^1$.
