Geodesic
On~integrability of the Banach indicatrix of a~smooth mapping
Izvestiya. Mathematics , Tome 25 (1985) no. 1, pp. 19-44.

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Let $f\colon\mathbf R^n\to\mathbf R^n$ be a mapping of class $C^{(l)}$ with compact support, and let $N(f,y)$ be the number of solutions of the equation $f(x)=y$. It is proved that if $p$, then $\int[N(f,y)]^p\,dy\infty$, and an example is given which shows that this integral can diverge if $p>l$. Bibliography: 9 titles. 
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S. A. Gulevich. On~integrability of the Banach indicatrix of a~smooth mapping. Izvestiya. Mathematics , Tome 25 (1985) no. 1, pp. 19-44. http://geodesic.mathdoc.fr/item/IM2_1985_25_1_a1/

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[9] Merkov A. B., “O nekotorykh svoistvakh gladkikh otobrazhenii”, Vestnik MGU. Ser. matem., 1979, no. 2, 63–69 | MR | Zbl