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A Fourier analytical characterization of the Hausdorff dimension of a closed set and of related Lebesgue spaces
Let Γ be a closed set in $ℝ^n$ with Lebesgue measure |Γ| = 0. The first aim of the paper is to give a Fourier analytical characterization of Hausdorff dimension of Γ. Let 0 < d < n. If there exist a Borel measure µ with supp µ ⊂ Γ …