(r, p)-capacity and Hausdorff measure on a local field

We will see a relationship between capacities and Hausdorff measure on local field. We can rely on technique in the existing capacity theory on the Euclidean space, however some counterparts of fundamental facts such as Whitney decomposition theorem and Wolff's inequality will be required. After establishing those counterparts, we will see some potential theoretic features based on the stable process on the field.