Almost all non-archimedean Kakeya sets have measure zero
Combinatorics
2016-08-10 v1 Number Theory
Probability
Abstract
We study Kakeya sets over local non-archimedean fields with a probabilistic point of view: we define a probability measure on the set of Kakeya sets as above and prove that, according to this measure, almost all non-archimedean Kakeya sets are neglectable according to the Haar measure. We also discuss possible relations with the non-archimedean Kakeya conjecture.
Cite
@article{arxiv.1608.02720,
title = {Almost all non-archimedean Kakeya sets have measure zero},
author = {Xavier Caruso},
journal= {arXiv preprint arXiv:1608.02720},
year = {2016}
}