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 \((∂_1m_1 f, ∂_2m_2 f,…, ∂_dm_d f)\) 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.
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Nikita P. Dobronravov (2024) studied this question.
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