%0 Journal Article
%T The Lebesgue Measure of the Julia Sets of Permutable Transcendental Entire Functions
%A Cunji Yang
%A Shaomin Wang
%J Advances in Pure Mathematics
%P 526-534
%@ 2160-0384
%D 2022
%I Scientific Research Publishing
%R 10.4236/apm.2022.129040
%X In 1958, Baker posed the question that if <em>f</em> and <em>g</em> 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 <em>f</em> and <em>g</em> are permutable transcendental entire functions, then <em>mes</em> (<em>J</em>(<em>f</em>)) = <em>mes</em> (<em>J</em>(<em>g</em>)). Moreover, we give some results about the zero measure of the Julia sets of the permutable transcendental entire functions family.
%K Transcendental Entire Function
%K Permutable Functions
%K Random Dynamics
%K Julia Set
%K Lebesgue Measure
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=119985