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math.LO2026
A Baire Category Approach to Besicovitch's Theorem and Measure Regularity
Emma Gruner, Jan Reimann
By reformulating the classical proof as a Baire Category argument, we show that Besicovitch's Theorem on the existence of subsets of finite Hausdorff measure is provable in $\maths…
math.LO2024★ 4 cited
Information vs Dimension -- an Algorithmic Perspective
Jan Reimann
This paper surveys work on the relation between fractal dimensions and algorithmic information theory over the past thirty years. It covers the basic development of prefix-free Kol…