Frostman's lemma provides a convenient tool for estimating the Hausdorff dimension of sets in mathematics, and more specifically, in the theory of fractal dimensions,[1] 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.
[2] A useful corollary of Frostman's lemma requires the notions of the s-capacity of a Borel set A ⊂ Rn, which is defined by (Here, we take inf ∅ = ∞ and 1⁄∞ = 0.
It follows from Frostman's lemma that for Borel A ⊂ Rn
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