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Corrected reference of Theorem 1.1
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ldiedering committed Jun 8, 2024
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Expand Up @@ -39,7 +39,7 @@ \chapter{Introduction}
\begin{theorem}[classical Carleson]
\label{classical-Carleson}
\leanok
\uses{piecewise-constant-approximation, convergence-for-smooth,
\uses{smooth-approximation, convergence-for-smooth,
control-approximation-effect}
Let $f$ be a $2\pi$-periodic complex-valued uniformly continuous function on $\mathbb{R}$ satisfying the bound $|f(x)|\le 1$ for all $x\in \mathbb{R}$. For all $0<\epsilon<1$, there exists a Borel set $E\subset [0,2\pi]$ with Lebesgue measure $|E|\le \epsilon$ and a positive integer $N_0$ such that for all $x\in [0,2\pi]\setminus E$ and all integers $N>N_0$, we have
\begin{equation}\label{aeconv}
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