Abstract
Let G be a simply connected, bounded domain on the plane with the boundary Γ and let P(Γ) be a uniform closure of polynomials on Γ. It is shown that the Rudin-Carleson Theorem about analytic extensions from zero measure boundary sets is valid for P(Γ) if and only if G is a Caratheodory domain and \({\bar G}\) does not separate the plane. These conditions are also equivalent to maximality of P(Γ) in C(Γ).
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