A Comparison of Gauge Dimension and Effective Dimension
Abstract
We characterize the gauge profile of $\mathcal{D}_s$, the set of reals with effective dimension $s$, and $\mathcal{D}_{\leq s}$, the set of reals with effective dimension $\leq s$. Let $W(s)$ be the set of reals that are $s$-well approximable. This gives us a separation between $\mathcal{D}_{\leq s}$ and $W(2/s)$ in terms of Hausdorff measure.
Fields of Study & Subjects
Computability
Logic
AI Algorithms
Mathematical Dynamics and Fractals
Advanced Topology and Set Theory
Publication details
- Journal / source
- arXiv (Cornell University)
- Publication date
- 31 January 2026
- Document type
- Preprint