Geodesic
Frostman lemma revisited
Nikita Dobronravov1
1St. Petersburg State University, Department of Leonhard Euler International Mathematical Institute
Annales Fennici Mathematici, Tome 49 (2024) no. 1, p. 303–318

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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.
DOI : 10.54330/afm.145356
Keywords: Hausdorff dimension, Frostman lemma, differentiable functions

Nikita Dobronravov  1

1 St. Petersburg State University, Department of Leonhard Euler International Mathematical Institute 
Nikita Dobronravov. Frostman lemma revisited. Annales Fennici Mathematici, Tome 49 (2024) no. 1, p. 303–318. doi: 10.54330/afm.145356
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