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