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This paper proves that if points $Z_1,Z_2,...$ are chosen independently andidentically using some measure $\mu$ from the unit circle in the complex plane,with $p_n(z) = (z-Z_1)(z-Z_2)...(z-Z_n)$, then the empirical distribution ofthe critical points of $p_n$ converges weakly to $\mu$.

On the Distribution of Critical Points of a Polynomial