Measure, Integration & Real Analysis · Problem 2E.15

Integration — Sheldon Axler

Mathematics — Measure Theory · lebesgue-measurable-borel-approximation

Problem

Suppose

B

is a Borel set and

f: B \to \mathbf{R}

is a Lebesgue measurable function. Show that there exists a Borel measurable function

g: B \to \mathbf{R}

such that

|\{x \in B : g(x) \neq f(x)\}| = 0.