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.
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@article{CML_2018__10_1_3_0,
author = {Xavier Caruso},
title = {Almost all non-archimedean {Kakeya} sets have measure zero},
journal = {Confluentes Mathematici},
pages = {3--40},
publisher = {Institut Camille Jordan},
volume = {10},
number = {1},
year = {2018},
doi = {10.5802/cml.44},
mrnumber = {3869009},
language = {en},
url = {https://cml.centre-mersenne.org/articles/10.5802/cml.44/}
}
TY - JOUR AU - Xavier Caruso TI - Almost all non-archimedean Kakeya sets have measure zero JO - Confluentes Mathematici PY - 2018 SP - 3 EP - 40 VL - 10 IS - 1 PB - Institut Camille Jordan UR - https://cml.centre-mersenne.org/articles/10.5802/cml.44/ DO - 10.5802/cml.44 LA - en ID - CML_2018__10_1_3_0 ER -
Xavier Caruso. Almost all non-archimedean Kakeya sets have measure zero. Confluentes Mathematici, Tome 10 (2018) no. 1, pp. 3-40. doi : 10.5802/cml.44. https://cml.centre-mersenne.org/articles/10.5802/cml.44/
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