Erdős problem 1040

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

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

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