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Erdős problem 1040

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For a closed infinite set F⊆CF \subseteq \mathbb{C}, let μ(F)\mu(F) be the infimum of ∣{z:∣f(z)∣<1}∣|\{z : |f(z)| < 1\}| over monic polynomials with zeros in FF. Is μ(F)\mu(F) determined only by the transfinite diameter of FF?

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