In mathematics, Dini's criterion is a condition for the pointwise convergence of Fourier series, introduced by Ulisse Dini (1880).
Dini's criterion states that if a periodic function
is locally integrable near
, then the Fourier series of
Dini's criterion is in some sense as strong as possible: if
is a positive continuous function such that
is not locally integrable near
, there is a continuous function
whose Fourier series does not converge at