On integrability of the Banach indicatrix of a smooth mapping

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 $p<l$, then $\int[N(f,y)]^p\,dy<\infty$, and an example is given which shows that this integral can diverge if $p>l$.
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