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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     author = {S. A. Gulevich},
     title = {On~integrability of the {Banach} indicatrix of a~smooth mapping},
     journal = {Izvestiya. Mathematics },
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     volume = {25},
     number = {1},
     year = {1985},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1985_25_1_a1/}
}
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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/