2 papers
math.MG2026
The sequence property for fractal dimensions
Kenneth Falconer, Yuyang Liu
For various definitions of fractal dimension that are finitely stable, including upper box dimension, upper intermediate dimensions and Assouad spectra, we show that, given a compa…
math.MG2026
On the Marstrand projection theorem for the Assouad spectrum
Kenneth J. Falconer, Jonathan M. Fraser, Antti Käenmäki
Marstrand's projection theorem states that the Hausdorff dimension of the orthogonal projection of a Borel set in the plane onto lines is constant almost surely. This property exte…