Let D = { z ∈ C :|z| < 1 } be the unit disk and T its boundary. We shall con- sider (injective) conformal maps f of D into C. For ζ∈ T we denote by f(ζ) the angular (= radial) limit if it exists and is finite. This holds for almost all ( ζ∈ T; even the exceptional set has zero logarithmic capacity, by the well-known Beur- ling theorem (see [Be; Po2, p.215]). Furthermore, the set { ζ∈ T: f(ζ) = a } has zero capacity for every a ∈ C [Du; Po2, p. 219]. A stronger condition is that f is continuous at ζ; that is f(z) -> f(ζ) as z -> ζ, z∈ D.
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