A Frostman-Type Lemma for Sets with Large Intersections, and an Application to Diophantine Approximation
We consider classes G(s)([0, 1]) of subsets of [0, 1], originally introduced by Falconer, that are closed under countable intersections, and such that every set in the class has Hausdorff dimension at least s. We provide a Frostman-type lemma to determine if a limsup set is in such a class. Suppose that E = lim supE(n) subset of [0, 1], and that mu(n) are probability measures with support in E-n.