Year: 2026
Type: preprint
Abstract: We introduce a spectrum of dimensions of measures, the \emph{packing intermediate dimensions} $\dim_{P,θ}μ$, $θ\in(0,1]$, of a Borel probability measure $μ$ on $\mathbb{R}^n$ and the \emph{quasi-Hausdorff dimension} $\dim_{qH}μ$. We show that this spectrum encodes the information on $μ$ that governs the packing dimension of its projections and Hölder images. First, $\dim_{qH}μ$ is the exact threshold for the packing dimension profiles of Falconer and Howroyd: for every real $0
Source: arXiv (Cornell University)
Author: Angelini, Nicolas
Language: English
Subfield: Mathematical Physics
Field: Mathematics
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7222006083