A stronger condition than continuous or uniformly continuous. A function f on an interval I (of the real line) is absolutely continuous if, for every positive number ε‎, there exists a positive number δ‎ so that for every finite sequence of pairwise disjoint subintervals of I with ${\sum }_k|y_k-x_k|<\delta$ then ${\sum }_k|f\left(y_k\right)-f\left(x_k\right)|<\epsilon$. Functions satisfying the Lipschitz condition are absolutely continuous. Absolutely continuous functions have a derivative almost everywhere (see almost all) which satisfies the Fundamental Theorem of Calculus. See also Cantor distribution.