Author(s)

Cunji Yang, Shaomin Wang

Department of Mathematics and Computer Science, Dali University, Dali, China.

In 1958, Baker posed the question that if f and g are two permutable transcendental entire functions, must their Julia sets be the same? In order to study this problem of permutable transcendental entire functions, by the properties of permutable transcendental entire functions, we prove that if f and g are permutable transcendental entire functions, then mes (J(f)) = mes (J(g)). Moreover, we give some results about the zero measure of the Julia sets of the permutable transcendental entire functions family.

Transcendental Entire Function, Permutable Functions, Random Dynamics, Julia Set, Lebesgue Measure

Yang, C. and Wang, S. (2022) The Lebesgue Measure of the Julia Sets of Permutable Transcendental Entire Functions. Advances in Pure Mathematics, 12, 526-534. doi: 10.4236/apm.2022.129040.