Geodesic
Proof of a~theorem of Lusin
Matematičeskie zametki, Tome 23 (1978) no. 1, pp. 61-66.

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In [1, 2], Lusin published a theorem (with proof) asserting that a very simple set constructed by him is not Borel. Lunina [3] discovered an error in Lusin's proof. It is proved that Lusin's theorem is nonetheless valid. 
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     author = {V. G. Kanovei},
     title = {Proof of a~theorem of {Lusin}},
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}
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V. G. Kanovei. Proof of a~theorem of Lusin. Matematičeskie zametki, Tome 23 (1978) no. 1, pp. 61-66. http://geodesic.mathdoc.fr/item/MZM_1978_23_1_a6/