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arXiv · 2602.00435

A Comparison of Gauge Dimension and Effective Dimension

Yiping Miao
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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.

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Yiping Miao. 2026-01-31. A Comparison of Gauge Dimension and Effective Dimension. https://arxiv.org/abs/2602.00435

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