Geodesic
A Remark on the Theorems of Lusin and Egoroff
Canadian mathematical bulletin, Tome 7 (1964) no. 2, pp. 291-295

Voir la notice de l'article provenant de la source Cambridge University Press

In this note we do not intend to establish new results but only to suggest avery simple proof of Lusin's theorem, direct for σ-finite regular measures,a proof that bypasses the usual procedure of first establishing this theoremfor sets of finite measure only. The proposed proof utilizes the notion ofsubuniform convergence, a method which seems not yet to have been used,despite its simplicity and adaptability. Simultaneously, a useful supplementto Egoroff's theorem will be obtained. 
Zakon, Elias. A Remark on the Theorems of Lusin and Egoroff. Canadian mathematical bulletin, Tome 7 (1964) no. 2, pp. 291-295. doi: 10.4153/CMB-1964-028-x
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