  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
$(\partial_1^{m_1} f, \partial_2^{m_2} f,\ldots, \partial_d^{m_d} f)$ 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.
