Comment by Gro-Tsen on Cesàro convergence of Fourier series for $f \in L^1(\mathbb{R} / \mathbb{Z})$

Here are two possible precise references for this very standard fact: Antoni Zygmund, Trigonometric Series, 3rd ed., III.3.9 (vol. 1, p. 90); or Yitzhak Katznelson, An Introduction to Harmonic Analysis, 3rd corr. ed., I.3.2 (p. 20).