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Critical values for Intermediate and Box dimension of projections and other images
Nicolas Angelini, Ursula Molter · 2025-01-28 · via math.PR updates on arXiv.org

Given a compact set $E\subset\mathbb{R}^d$ we investigate for which values of $m$ we have that $\dim_θP_V(E)=m$ or $\dim_θP_V(E)=\dim_θE$ for $γ_{d,m}-$almost all $V\in G(d,m)$. Our result can be extended to more general functions that include orthogonal projections and fractional Brownian motion. As a particular case, letting $θ=1$, the results are valid for the Box dimension.

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