Let $f \in L^1[0, 1]$, then we know we can write $$f = \sum_{n \in \mathbb{Z}} \hat{f}(n) e^{2 \pi i n t},$$ where we have convergence in $L^1$-norm. My question is, do we have unconditional convergence? That is, will the same series converge to $f$ despite rearrangements?
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