What would you like to understand?

The estimation lemma (ML inequality) is applied by bounding the absolute value of the integral of $f(w) - f(a)$ over the path $\gamma_z$ by the supremum of $|f(w) - f(a)|$ on $\gamma_z$ multiplied by the length of the path $\gamma_z$. Since $\gamma_z$ is the straight line segment from a to z, its length is $|z - a|$.

Conditions: The path $\gamma_z$ is a rectifiable contour (specifically, a straight line segment).; The function f is continuous on $\gamma_z$.; The integrand is $f(w) - f(a)$.

The estimation lemma (ML inequality) is applied by bounding the absolute value of the integral of $f(w) - f(a)$ over the path $\gamma_z$ by the supremum of $|f(w) - f(a)|$ on $\gamma_z$ multiplied by the length of the path $\gamma_z$. Since $\gamma_z$ is the straight line segment from a to z, its length is $|z - a|$.

Conditions: The path $\gamma_z$ is a rectifiable contour (specifically, a straight line segment).; The function f is continuous on $\gamma_z$.; The integrand is $f(w) - f(a)$.