L2 norm convergence
= L2 norm convergence
{title2=$\|f_n-f\|_2\to0$}
A sequence in <L2 space> converges in its <L2 norm> when $\int|f_n-f|^2\,d\mu\to0$. This concerns the integral of the squared error and need not imply <pointwise convergence>. In particular a complete <Fourier sine basis> reconstructs each odd <L2 function> in this norm, while pointwise claims about its <Fourier series> require additional hypotheses.