What is a compact set $A⊂I$ that satisfies the Lusin's theorem statement about $f$ for $ε > 0$?
2026-03-25 06:00:27.1774418427
An apparent counterexample to Lusin's theorem
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Hint: Choose compact sets $A_1\subset E, A_2\subset E^c$ with the appropriate Lusin property. Then $\chi_{A_1}$ is continuous on $A_1\cup A_2.$