f : [a,b] → ℝ is absolutely continuous iff ∀ε>0 ∃δ>0 such that for any finite collection of disjoint intervals (x_i,y_i) with Σ(y_i−x_i)<δ, Σ|f(y_i)−f(x_i)|<ε. Equivalent to f being a Lebesgue integral of its derivative.
f : [a,b] → ℝ is absolutely continuous iff ∀ε>0 ∃δ>0 such that for any finite collection of disjoint intervals (x_i,y_i) with Σ(y_i−x_i)<δ, Σ|f(y_i)−f(x_i)|<ε. Equivalent to f being a Lebesgue integral of its derivative.