In mathematics, the Dini–Lipschitz criterion is a sufficient condition for the Fourier series of a periodic function to converge uniformly at all real numbers. It was introduced by Ulisse Dini , as a strengthening of a weaker criterion introduced by Rudolf Lipschitz . The criterion states that the Fourier series of a periodic function f converges uniformly on the real line if where is the modulus of continuity of f with respect to .