Measure, Integration & Real Analysis · Problem 2A.7

Measures — Sheldon Axler

Mathematics — Measure Theory · outer-measure-union-of-two-intervals

Problem

Suppose

a, b, c, d

are real numbers with

a < b

and

c < d

. Prove that

|(a, b) \cup (c, d)| = (b - a) + (d - c) \text{ if and only if } (a, b) \cap (c, d) = \varnothing.