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The set of Plessner Points of a holomorphic function
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Theorem. For each number α(0≤α≤2π) and each closed set A on C = {z:|z|=1} with measure α, there exists a holomorphic function F(z) in D = {z : |z|<1} whose set of Plessner Points is dense on C, has measure α, and each point of A is a Plessner Point of F(z).

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