On a sufficient condition for integrability of the banach indicatrix of a smooth mapping

Sufficient conditions are given for the convergence of integrals of the form $\int_{\mathbf R^k}(N(f,y))^p\,dy$, where $f\colon\mathbf R^n\to\mathbf R^k$ is a map with compact support with $k\leqslant n$ and $N(f,y)$ is the number of connected components of the level set $\{x:f(x)=y\}$.
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