# 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