Author

Amir Algom

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Preprint Aug 2026

Ergodic $\times p$-invariant measures on $\mathbb{T}^2$ with no dimension dropping projections

Fix an integer $p\geq 2$ and $0<s<1$. We construct an ergodic $\times p$-invariant measure $\mu$ on $\mathbb T^2$ of dimension $s$, such that every line projection preserves dimension, including when the corresponding projected IFS has exact overlaps. In fact, our measure assigns mass $O(w^s)$ to every planar tube of w...

Amir Algom · 0 citations