Let $f$ be a transcendental entire function. The escaping set $I(f)$ consists of those points that tend to infinity under iteration of $f$. We show that $I(f)$ is not $\sigma$-compact, resolving a question of Rippon from 2009.
The dynamics of semigroups of transcendental entire functions II
Lebesgue measure of escaping sets of transcendental entire functions in the Eremenko-Lyubich class
The escaping set of the exponential
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