Let Δ = {z ∈ C : |z| < 1}. Let Bo denote the set of functions φ analytic in Δ and satisfying |φ(z)| < 1. φ(0) = 0. Suppose F is analytic and univalent in Δ and maps it onto a convex domain D. Let s(F) = {F o φ : φ ∈ B_0}, and let Es(F) denote the set of extreme points of s(F). For every f ∈ s(F), let f(θ) = lim_(r→1) f(re~(iθ)) be the boundary function of f, let {f(θ)} denote the set of all existing radial limits of f, and define λ(θ) = dist(f(θ), (partial deriv)F(Δ)) almost everywhere on (partial deriv)Δ. We show two properties of extreme points of s(F). In the case when D is the interior of a convex polygon we prove that (partial deriv)D is contained in {f(θ)} is a necessary condition for f ∈ Es(F). We also prove that if D is any convex domain and the boundary function f(θ) of f, f ∈ Es(F), is continuous then there exists a point e ∈ E(partial deriv)D such that for every neighbourhood N(e) of e ∫_(A_(N(e))) log λ(θ)dθ = -∞, where A_(N(e)) = {θ ∈ (partial deriv)Δ : f(θ) ∈ N(e)}.
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