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math.CA2025
Hausdorff measure of cartesian product of Cantor sets
Siyuan Guo, Taylor Jones
Hausdorff measure and Hausdorff dimension are useful tools to describe fractals. This paper investigates the bounds on the -dimensional Hausdorff measure of the -fold…
math.CA2022
Box-counting dimension and differentiability of box-like statistically self-affine functions
Pieter Allaart, Taylor Jones
We consider a class of "box-like" statistically self-affine functions, and compute the almost-sure box-counting dimension of their graphs. Furthermore, we consider the differentiab…