The precise representative for the gradient of the Riesz potential of a finite measure

Julià Cufí, Augusto C. Ponce, Joan Verdera

Given a finite nonnegative Borel measure $m$ in ${\mathbb{R}}^d$, we identify the Lebesgue set $\mathcal{L}(V_s)\subset {\mathbb{R}}^d$ of the vector-valued function $$V_{s}(x)…