2 papers
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.LO2023
Normality, Relativization, and Randomness
Wesley Calvert, Emma Grunner, Elvira Mayordomo +2
Normal numbers were introduced by Borel and later proven to be a weak notion of algorithmic randomness. We introduce here a natural relativization of normality based on generalized…