Almost-nowhere intersection of Cantor sets, and sufficient sampling of their cumulative distribution functions
Classical Analysis and ODEs
2019-12-12 v1
Abstract
Cantor sets are constructed from iteratively removing sections of intervals. This process yields a cumulative distribution function (CDF), constructed from the invariant measure associated with their iterated function systems. Under appropriate assumptions, we identify sampling schemes of such CDFs, meaning that the underlying Cantor set can be reconstructed from sufficiently many samples of its CDF. To this end, we prove that two Cantor sets have almost-nowhere (with respect to their respective invariant measures) intersection.
Keywords
Cite
@article{arxiv.1912.05498,
title = {Almost-nowhere intersection of Cantor sets, and sufficient sampling of their cumulative distribution functions},
author = {Allison Byars and Evan Camrud and Steven N. Harding and Sarah McCarty and Keith Sullivan and Eric S. Weber},
journal= {arXiv preprint arXiv:1912.05498},
year = {2019}
}