# $L_{p}$ norm sequence convergence does not imply pointwise convergence | ðŸ—– nosplit | â†‘ parent "Fourier basis is complete for $L_{2}$" | 41

There are explicit examples of this. We can have ever thinner disturbances to convergence that keep getting less and less area, but never cease to move around.

If it does converge pointwise to something, then it must match of course.