Measure, Integration & Real Analysis · Problem 2B.24

Measures — Sheldon Axler

Mathematics — Measure Theory · borel-sets-monotone-functions

Problem

Suppose

f : \mathbf{R} \to \mathbf{R}

is a strictly increasing function and

B \subseteq \mathbf{R}

is a Borel set. Prove that

f(B)

is a Borel set.