Algorithmic randomness and Fourier analysis

Suppose $1 < p < \infty$. Carleson's Theorem states that the Fourier series of any function in $L^p[-π, π]$ converges almost everywhere. We show that the Schnorr random points are precisely those that satisfy this theorem for every $f \in L^p[-π, π]$ given natural computability conditions on $f$ and $p$.

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