# Fourier basis is complete for $L_{2}$ | ðŸ—– nosplit | â†‘ parent "Riesz-Fischer theorem" | 55, 2, 230

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: $L_{p}$ norm sequence convergence does not imply pointwise convergence.