Measure, Integration & Real Analysis · Problem 2D.1
Integration — Sheldon Axler
Mathematics — Measure Theory · lebesgue-measure-borel-sets
Problem
(a) Show that the set consisting of those numbers in (0,1) that have a decimal expansion containing one hundred consecutive 4s is a Borel subset of R.
(b) What is the Lebesgue measure of the set in (a)?