An Important Lebesgue Non-Measurable Function

Since if we have a function f : R -> R continuous and a function g : R -> R Lebesgue measurable does not necessarily result that the function g circle f is Lebesgue measurable, with the help of Cantor's set we will constructed a Lebesgue measurable function h : R -> R and a continuous function u : R -> R, such that the function h circle u:R -> R is not Lebesgue measurable. (C) 2020 The Authors. Published by Elsevier B.V.