Abstract
Given a compact set of real numbers, a random -diffeomorphism is constructed such that the image of any measure concentrated on the set and satisfying a certain condition involving a real number , almost surely has Fourier dimension greater than or equal to . This is used to show that every Borel subset of the real numbers of Hausdorff dimension is -equivalent to a set of Fourier dimension greater than or equal to . In particular every Borel set is diffeomorphic to a Salem set, and the Fourier dimension is not invariant under -diffeomorphisms for any .
Citation
Fredrik Ekström. "Fourier dimension of random images." Ark. Mat. 54 (2) 455 - 471, October 2016. https://doi.org/10.1007/s11512-016-0237-3
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