Measure, Integration & Real Analysis · Problem 2D.12

Integration — Sheldon Axler

Mathematics — Measure Theory · lebesgue-measurability-characterization

Problem

Suppose

b < c

and

A \subseteq (b, c)

. Prove that

A

is Lebesgue measurable if and only if

|A| + |(b,c) \setminus A| = c - b