Measure, Integration & Real Analysis · Problem 2B.12

Measures — Sheldon Axler

Mathematics — Measure Theory · borel-set-continuity-points

Problem

Suppose

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

is a function. Show that the set of points at which

f

is continuous is the intersection of a sequence of open sets, and thus is a Borel set.