Measure, Integration & Real Analysis · Problem 2B.18

Measures — Sheldon Axler

Mathematics — Measure Theory · borel-measurable-functions

Problem

Suppose

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

is differentiable at every element of

\mathbf{R}

. Prove that

f'

is a Borel measurable function from

\mathbf{R}

\mathbf{R}