Fractal Intersections and Products via Algorithmic Dimension
Computational Complexity
2021-03-02 v6 Metric Geometry
Abstract
Algorithmic fractal dimensions quantify the algorithmic information density of individual points and may be defined in terms of Kolmogorov complexity. This work uses these dimensions to bound the classical Hausdorff and packing dimensions of intersections and Cartesian products of fractals in Euclidean spaces. This approach shows that two prominent, fundamental results about the dimension of Borel or analytic sets also hold for arbitrary sets.
Cite
@article{arxiv.1612.01659,
title = {Fractal Intersections and Products via Algorithmic Dimension},
author = {Neil Lutz},
journal= {arXiv preprint arXiv:1612.01659},
year = {2021}
}