Lemma: Let A be a Borel subset of Rn, 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 ⊂ Rn, which is defined by