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Mergelyan pairs for harmonic functions

Let Q C Rn be open and E C Q be a bounded set which is closed relative to Q. We characterize those pairs (Q, E) such that, for each harmonic function h on Q which is uniformly continuous on E, there is a sequence of harmonic polynomials which converges to h uniformly on E. As an immediate corollary we obtain a characterization of Mergelyan pairs for harmonic functions.