Research proof index

Let $f$ be $2\pi$-periodic and belong to $L^q((0,2\pi])$ for some $q>1$. Given thresholds $\delta,\varepsilon>0$, there is an index $N_0$ such that the set where the tail error $\sup_{N>N_0}\lVert f(x)-S_Nf(x)\rVert$ exceeds $\delta$ has measure at most $\varepsilon$.