English

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}
}
R2 v1 2026-06-22T15:15:39.059Z