A note on dyadic Hausdorff capacities

In this paper, the authors give a counterexample to show that the classical dyadic Hausdorff capacity on Rn when n?2 and 0<d?n−1 is not a capacity in the sense of Choquet. A variant of the classical dyadic Hausdorff capacity, , is then introduced and is further proved to be a capacity in the sense of Choquet.