Frostman lemma revisited - Dobronravov, Nikita (Annales Fennici Mathematici, 2024)
We study sharpness of various generalizations of Frostman’s lemma. These generalizations provide better estimates for the lower Hausdorff dimension of measures. As a corollary, we prove that if a generalized anisotropic gradient \((_1^m_1 f, _2^m_2 f,…, _d^m_d f)\) of a function \(f\) in \(d\) variables is a measure of bounded variation, then this measure is absolutely continuous with respect to the Hausdorff \(d-1\) dimensional measure.