Harmonic measure of an annulus
= Harmonic measure of an annulus
{title2=$\omega_{A(r,1)}(z,\mathbb T)=\log(|z|/r)/\log(1/r)$}
For $0<r<1$, the <harmonic measure> of the outer circle of $r<|z|<1$ is the title expression. The function $\log|z|$ is harmonic away from zero; the normalization gives boundary values zero on the inner circle and one on the outer circle. Uniqueness of the <Dirichlet problem> proves the formula. A <conformal map> to an annulus transports it to a <doubly connected domain>.