Measure, Integration & Real Analysis · Problem 2D.13

Integration — Sheldon Axler

Mathematics — Measure Theory · lebesgue-measurability-characterization-intervals

Problem

Suppose

A \subseteq \mathbf{R}

. Prove that

A

is Lebesgue measurable if and only if

|(-n,n) \cap A| + |(-n,n) \setminus A| = 2n

for every

n \in \mathbf{Z}^+