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In this paper we study the $s$-dimensional Riesz transform of a finitemeasure $\mu$ in $\mathbf{R}^d$, with $s\in (d-1,d)$. We show that theboundedness of the Riesz transform of $\mu$ implies that a nonlinear potentialof exponential type is finite $\mu$-almost everywhere. It appears to be thefirst result of this type for $s>1$.

The fractional Riesz transform and an exponential potential