= Fourier basis is complete for $\LTwo$
{id=fourier-basis-is-complete-for-l2}
{c}
https://math.stackexchange.com/questions/316235/proving-that-the-fourier-basis-is-complete-for-cr-2-pi-c-with-l2-norm
<Riesz-Fischer theorem> is a norm version of it, and <Carleson's theorem> is stronger pointwise almost everywhere version.
Note that the <Riesz-Fischer theorem> is weaker because the pointwise limit could not exist just according to it: <lp norm sequence convergence does not imply pointwise convergence>.