Suppose that f is increasing and let P a partition where x⸤i⸥−x⸤i−1⸥ = (b−a)/n.
∀ε>0 ∃n∈ℕ such that n>(f(b)−f(a))·(b−a)/ε.
｢sup(f(x))ƧP[a,b]｣
− ｢inf(f(x))ƧP[a,b]｣
= ｢(sup(f(x))−inf(f(x)))ƧP[a,b]｣
= ｢(f(max(x))−f(min(x)))ƧP[a,b]｣
= (f(b)−f(a))·(b−a)/n
< ε
