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

Integration — Sheldon Axler

Mathematics — Measure Theory · borel-measurable-no-continuous-restriction

Problem

Give an example of a Borel measurable function ff from R\mathbf{R} to R\mathbf{R} such that there does not exist a set B⊆RB \subseteq \mathbf{R} such that ∣R∖B∣=0|\mathbf{R} \setminus B| = 0 and f∣Bf|_B is a continuous function on BB.

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