Geodesic
The $N^{-1}$-property of maps and Luzin's condition $(N)$
Matematičeskie zametki, Tome 58 (1995) no. 3, pp. 411-418.

Voir la notice de l'article provenant de la source Math-Net.Ru

A function $f\colon G\to\mathbb R^n$, where $G$ is an open set in $\mathbb R^n$, has the $N^{-1}$-property if for all $E\subset\mathbb R^n$ we have $\bigl\{|E|=0\Rightarrow|f^{-1}(E)|=0\bigr\}$ ($|\cdot|$ is the Lebesgue measure). The article is concerned with the relations between the $N^{-1}$-property of functions, the maximal rank of derivatives, and the differentiability almost everywhere of composite functions. 
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     author = {S. P. Ponomarev},
     title = {The $N^{-1}$-property of maps and {Luzin's} condition $(N)$},
     journal = {Matemati\v{c}eskie zametki},
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}
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S. P. Ponomarev. The $N^{-1}$-property of maps and Luzin's condition $(N)$. Matematičeskie zametki, Tome 58 (1995) no. 3, pp. 411-418. http://geodesic.mathdoc.fr/item/MZM_1995_58_3_a8/

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