could anybody will help me to do this problems:
- Let $\mathcal D$ be the unit disk a Set $E\subseteq\partial\mathcal D$ has harmonic measure identically $0$ with respect to $\mathcal D$. What can you conclude about $E$?
- Let $\Omega\subseteq\mathbb C$ be a domain and let E \text{ and } E'\subseteq\Omega such that \omega(z,\Omega,E)\ge\omega(z,\Omega,E') \forall z\in\Omega. What can you conclude about $E$ and E'?
Problems are taken from Respected Stephen Krantz's Geometric function theory book chapter9.