Measure, Integration & Real Analysis · Problem 2B.11

Measures — Sheldon Axler

Mathematics — Measure Theory · sigma-algebra-borel-subset-restriction

Problem

Suppose

X \subseteq \mathbf{R}

is a Borel set. Show that the

\sigma

-algebra on

X

consisting of all Borel subsets of

\mathbf{R}

contained in

X

equals the

\sigma

-algebra

\{E \cap X : E \text{ is a Borel subset of } \mathbf{R}\}