Let $[a, b] \subseteq \mathbb{R}$ be a D544: Closed real interval such that

(i)	$f : [a, b] \to \mathbb{R}$ is a D4364: Real function on $[a, b]$

Then $f$ is absolutely continuous if and only if $$\begin{equation} \forall \, \varepsilon > 0 : \exists \, \delta > 0 : \forall \, N \in 1, 2, 3, \ldots : \forall \, \text{pairwise disjoint } [a_1, b_1], \ldots, [a_N, b_N] \subseteq [a, b] \left( \sum_{n = 1}^N |b_n - a_n| < \delta \quad \implies \quad \sum_{n = 1}^N |f(b_n) - f(a_n)| < \infty \right) \end{equation}$$