Measure, Integration & Real Analysis · Problem 2D.10

Integration — Sheldon Axler

Mathematics — Measure Theory · lebesgue-measure-disjoint-sets

Problem

Prove that if

A

and

B

are disjoint subsets of

\mathbf{R}

and

B

is Lebesgue measurable, then

|A \cup B| = |A| + |B|