4 problems

Quasi-Assouad dimension conjecture. The quasi-Assouad dimension of $F$, and therefore its Assouad spectrum, always coincides with the Hausdorff dimension of $F$.

Let $u$ be a near-$d$-regular measure on $mathbb{R}^{2}$, let $0leq s<d$, and let $mathsigma$ be a Borel probability measure on $S^{1}$. Suppose that for $mathsigma$-almost every…

Let $F\subseteq\mathbb{R}^d$. Denote by $\overline{\dim}_{\mathrm{A}}^\theta F$ and $\dim_{\mathrm{A}}^\theta F$ the upper and ordinary Assouad spectra, respectively. Eventual coin…

Assouad-dimension conjecture. For all such Takagi functions,