The talk is about a version of the McKay correspondence in positive or mixed characteristic. Roughly speaking, this version gives an equality between a weighted count of extensions of a local field and a weighted count of rational points of a variety over a finite field (with respect to "stringy weights"). In a particular example, it relates mass formulas of Serre and Bhargava with the Hilbert scheme of n points on an affine plane. A proof of this result is based on p-adic measures. The talk is partly based on a joint work with Melanie Machett Wood.