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Bounding the Dimension of Points on a Line (1612.00143v3)
Published 1 Dec 2016 in cs.CC and math.CA
Abstract: We use Kolmogorov complexity methods to give a lower bound on the effective Hausdorff dimension of the point (x, ax+b), given real numbers a, b, and x. We apply our main theorem to a problem in fractal geometry, giving an improved lower bound on the (classical) Hausdorff dimension of generalized sets of Furstenberg type.