The capacity γ

The capacity γ+ of a compact set \(E \subset \mathbb{C}\) is \(\gamma+(E) := \sup \{\mu(E) : {\rm{supp}}(\mu) \subset E, \|C\mu\|_{L}{^{\infty}}_{(\mathbb {C})} \leq 1\}\), and the capacity γ+ of an arbitary set \( A \subset {\mathbb{C}}\) is defined as \( \gamma+(A) = \sup\{\gamma+(E) : E \subset A, E \ {\rm{compact}}\}.\)