30 citations · 30 across the 6 of their papers we have counts for
6 papers
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…
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…
Intermediate dimensions -- a survey
Kenneth J. Falconer
This article surveys the -intermediate dimensions that were introduced recently which provide a parameterised continuum of dimensions that run from Hausdorff dimension when $θ=0…
Higher moments for random multiplicative measures
K. J. Falconer
We obtain a condition for the -convergence of martingales generated by random multiplicative cascade measures for without any self-similarity requirements on the cascade…
Attractors of directed graph IFSs that are not standard IFS attractors and their Hausdorff measure
G. C. Boore, K. J. Falconer
For directed graph iterated function systems (IFSs) defined on R, we prove that a class of 2-vertex directed graph IFSs have attractors that cannot be the attractors of standard (1…
Multifractional, multistable, and other processes with prescribed local form
K. J. Falconer, J. Levy Vehel
We present a general method for constructing stochastic processes with prescribed local form. Such processes include variable amplitude multifractional Brownian motion, multifracti…