First let us define analytic capacity: Let E\in \mathbb{C} is compact, let U_E be the collection of functions f holomorphic on \hat{\mathbb{C}} - E ( \hat{\mathbb{C}} is \mathbb{C} \cup\infty) and f(\infty) = 0 and \sup{|f(z)|}\leq 1; the analytic capacity of E is defined as :

 \gamma (E) = \sup_{f\in U_E}{f'(\infty)}.

Now here is my question:

If E_1, E_2 are disjoint compact sets which can be separated by a line l (i.e. l\cap E_j = \emptyset, j = 1,2), then show that:

\gamma(E_1\cup E_2)\leq \gamma(E_1) + \gamma(E_2) .

Thank you in advance!