Seminar: Gauge Dimension and the Borel Hierarchy

Mercoledì, 10 Settembre, 2025 - 15:00

AULA 456
15:00-16:00; September 10, 2025

 

Theodore A. Slaman
Professor Emeritus
Department of Mathematics – University of California at Berkeley – USA

 

We exhibit a low-level Borel set whose gauge dimension, a refinement of Hausdorff dimension, cannot be duplicated by any closed set. is the set of sufficiently generic reals for a measure-theoretic family of closed sets.  This answers a question of C.A. Rogers and raises the question of whether there is a hierarchy of gauge dimension profiles which are proper within the Borel Hierarchy.