Dini condition

Dini condition

[′dē·nē kən¦didh·ən]
(mathematics)
A condition for the convergence of a Fourier series of a function ƒ at a number x, namely, that the limits of ƒ at x on the left and right, ƒ (x-) and ƒ (x +), both exist, and that the function given by the absolute value of [ƒ(x + t) - ƒ (x +) + ƒ (x-t) - ƒ (x-)]/ t be integrable on some closed interval, -dtd, where d is a positive number.