Almost all non-archimedean Kakeya sets have measure zero
Confluentes Mathematici, Tome 10 (2018) no. 1, pp. 3-40.

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.

Reçu le : 2016-05-09
Accepté le : 2017-09-22
Publié le : 2018-09-10
DOI : https://doi.org/10.5802/cml.44
Classification : 05B30,  51E20,  60B11,  11K41
Mots clés: Kakeya set, discrete valuation fields
@article{CML_2018__10_1_3_0,
     author = {Xavier Caruso},
     title = {Almost all non-archimedean Kakeya sets have measure zero},
     journal = {Confluentes Mathematici},
     publisher = {Institut Camille Jordan},
     volume = {10},
     number = {1},
     year = {2018},
     pages = {3-40},
     doi = {10.5802/cml.44},
     language = {en},
     url = {cml.centre-mersenne.org/item/CML_2018__10_1_3_0/}
}
Caruso, Xavier. 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/item/CML_2018__10_1_3_0/

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