For exponential polynomials satisfying certain argument conditions and a technical condition in the opposite-argument case, the complement of the Julia set intersect the fast escaping set has finite Lebesgue measure.
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Exponential polynomials with Fatou and non-escaping sets of finite Lebesgue measure
For exponential polynomials satisfying certain argument conditions and a technical condition in the opposite-argument case, the complement of the Julia set intersect the fast escaping set has finite Lebesgue measure.