Estimation lemma
In complex analysis, the estimation lemma, also known as the ML inequality (ML for Max times Length), gives an upper bound for a contour integral. If f is a complex-valued, continuous function on the contour Γ and if its absolute value |f (z)| is bounded by a constant M for all z on Γ, then | ∫ Γ f ( z ) d z | ≤ M l ( Γ ) , {\displaystyle \left|\int _{\Gamma }f(z)\,dz\right|\leq M\,l(\Gamma ),} where l(Γ) is the arc length of Γ. In particular, we may take the maximum M := sup z ∈ Γ | f ( z ) | {\displaystyle M:=\sup _{z\in \Gamma }|f(z)|} as upper bound.