Fourier dimension of random images
Given a compact set of real numbers, a random Cm + α-diffeomorphism is constructed such that the image of any measure concentrated on the set and satisfying a certain condition involving a real number s, almost surely has Fourier dimension greater than or equal to s/ (m+ α). This is used to show that every Borel subset of the real numbers of Hausdorff dimension s is Cm + α-equivalent to a set of F