Source: cirosantilli/riesz-fischer-theorem
= Riesz-Fischer theorem
{c}
{wiki=Riesz–Fischer_theorem}
A measurable function defined on a closed interval is square integrable (and therefore in <l2>) if and only if <Fourier series> converges in <l2> norm the function:
$$
\lim_{N \to \infty} \left \Vert S_N f - f \right \|_2 = 0
$$