ABSTRACT

We introduce next certain “lower dimensional” measures on Rn, which allow us to measure certain “very small” subsets of Rn. These are the Hausdorff measures Hs, defined in terms of the diameters of various efficient coverings. The idea is that A is an “s-dimensional subset” of Rn if 0 < Hs(A) <∞, even if A is very complicated geometrically.