We prove an analogue of the classical Bernstein polynomial inequality on a compact subset E of the real line. The Lipschitz continuity of the Green function for the complement of E with respect to the extended complex plane and the differentiability at a point of E of a special, associated with E, conformal mapping of the upper half-plane onto the comb domain play crucial role in our investigation. (C) 2019 Elsevier Inc. All rights reserved.
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