\Omega$ such that $$\hat{u}(z) = \int _{\partial \Omega} u d \omega_{z}, \hspace{.2in}
u \in C(\partial \Omega).$$ The measure $\omega_{z}$ is called the harmonic measure of $\Omega$ evaluated at $z$. The harmonic measures evaluated at two different points are boundedly equivalent. We shall use $\omega_{\Omega}$ to denote a harmonic measure of $\Omega$.

[*Hypodirichlet algebras*]{}. A closed subalgebra $\cal B$ of $C(K)$ is said to be a hypo-Dirichlet algebra, if the uniform closure of $ Re(\cal B)= \{ Re(f): f \in
\cal B\}$ has finite codimension in $C_{R}(K) = \{f: f\in C(K)$ and $f$ is real$\}$ and the linear span of log$|\cal B^{-1}|$ is uniformly dense in $C_{R}(K)$, where $\cal B^{-1}$ is the subset in $\cal B$ consisting of invertible elements. A function algebra $\cal B$ is called a Dirichlet algebra if $Re(B)$ is uniformly dense in $C_{R}(K)$. Clearly, a Dirichlet algebra is also a hypo-Dirichlet algebra. An good example is that $R(K)$ is hypo-Dirichlet if [**C**]{} $\setminus
K$ has only finitely many components. This covers a large class of domains that have been studied. If $R(K)$ is a hypo-Dirichlet algebra, then $A(K)=R(K)$ [@ga p. 116]. [*Peak points*]{}. A point $a\in K$ is a peak point for a function algebra $\cal B 