Frostman lemma revisited
Abstract
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 (∂1m1 f, ∂2m2 f,…, ∂dmd 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.
0
Turn this paper into a full lesson
ArcXiv compiles a staged curriculum from this paper: 8-12 lessons across beginner → advanced, synthesised section guides, visuals, flashcards, a quiz, exercises, and on-demand deep dives per section. Grounded in the abstract, never invented.