Measure, Integration & Real Analysis · Problem 2B.28

Measures — Sheldon Axler

Mathematics — Measure Theory · borel-measurable-functions

Problem

Suppose

f : B \to \mathbf{R}

is a Borel measurable function. Define

g : \mathbf{R} \to \mathbf{R}

g(x) = \begin{cases} f(x) & \text{if } x \in B, \\ 0 & \text{if } x \in \mathbf{R} \setminus B. \end{cases}

Prove that

g

is a Borel measurable function.