  Let p be a monic polynomial in one complex variable and K a measurable subset
of the complex plane. In terms of the area of K, we give an upper bound on the
area of the preimage of K under p and a lower bound on the area of the image of
K under p, (counted with multiplicity). Both bounds are sharp. The former
extends an inequality of Polya. The proof uses Carleman's isoperimetric
inequality for plane condensers. We include a summary of the necessary
potential theory.
