Frostman lemma

In mathematics, and more specifically, in the theory of fractal dimensions, Frostman's lemma provides a convenient tool for estimating the Hausdorff dimension of sets.
Lemma: Let "A" be a Borel subset of R"n", and let "s" > 0. Then the following are equivalent:
Otto Frostman proved this lemma for closed sets "A" as part of his PhD dissertation at Lund University in 1935. The generalization to Borel sets is more involved, and requires the theory of Suslin sets.
A useful corollary of Frostman's lemma requires the notions of the "s"-capacity of a Borel set "A" ⊂ R"n", which is defined by
(Here, we take inf ∅ = ∞ and  = 0. As before, the measure formula_3 is unsigned.) It follows from Frostman's lemma that for Borel "A" ⊂ R"n"