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For potentials $U_K^T=K*T$, where $K$ and $T$ are certain Schwartz distributions, an inversion formula for $T$ is derived. Convolutions and Fourier transforms of distributions in $\left({\mathbf{D}}_L^{\text{'}}p\right)$-spaces are used. It is shown that the equilibrium distribution with respect to the Riesz kernel of order $\alpha$, $0\<\alpha \<m$, of a compact subset $E$ of ${\mathbf{R}}^m$ has the following property: its restriction to the interior of $E$ is an absolutely continuous measure with analytic density which is expressed by an explicit formula.