We give conditions ensuring that the Fatou set and the complement of the fast escaping set of an exponential polynomial f both have finite Lebesgue measure. Essentially, these conditions are designed such that $|f(z)|\ge \exp (|z|^\alpha )$ for some $\alpha>0$ and all z outside a set of finite Lebesgue measure.

中文翻译：

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具有 Fatou 和非转义有限 Lebesgue 测度集的指数多项式

我们给出条件确保法头集和指数多项式的快速转义集的补集F两者都有有限的勒贝格测度。本质上，这些条件的设计使得$|f(z)|\ge \exp (|z|^\alpha )$对于一些$\alpha>0$和所有z在一组有限 Lebesgue 测度之外。