 L2 norm convergence

A sequence in L2 space converges in its L2 norm when $\int |f_n-f{|}^{2}d\mu \to 0$. 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.