The logarithmic capacity of a compact set E in the complex plane is given by γ(E) = e^(-V(E)), where V(E) = inf_ν integral_(E×E) ln1/( left bracketing bar u - v right bracketing bar ) d ν(u) d ν(v), and ν runs over each probability measure on E. The quantity V(E) is called the Robin's constant of E and the set E is said to be polar if V(E) = + ∞ or equivalently, γ(E) = 0.

conformal radius | transfinite diameter