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Let $f: \mathbb{R} \to \mathbb{R}$ be the characteristic function of a subset $A \subseteq \mathbb{R}$ which is analytic but not Borel. Then $f$ is universally measurable but not Borel.
Let $f: \mathbb{R} \to \mathbb{R}$ be the characteristic function of a subset $A \subseteq \mathbb{R}$ which is analytic but Borel. Then $f$ is universally measurable but not Borel.