Let $f(z)$ be a non-constant entire function such that, for some $c$, the set $E(c)=\{z:|f(z)|>c\}$ has finite measure. What is the minimum growth rate of $f(z)$?If $E(c)$ has finite measure then must there exist $c^{\prime }<c$ such that $E(c^{\prime })$ has finite measure?