Published articles
no. 1
Almost all non-archimedean Kakeya sets have measure zero
Xavier Caruso1
1 Université Rennes 1, IRMAR, Campus de Beaulieu, 35042 Rennes Cedex
Confluentes Mathematici, Volume 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.

Received:
Accepted:
Published online:
DOI: 10.5802/cml.44
Classification: 05B30, 51E20, 60B11, 11K41
Mots-clés : Kakeya set, discrete valuation fields

Xavier Caruso 1

1 Université Rennes 1, IRMAR, Campus de Beaulieu, 35042 Rennes Cedex
License: CC-BY-NC-ND 4.0
Copyrights: The authors retain unrestricted copyrights and publishing rights 
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Xavier Caruso. Almost all non-archimedean Kakeya sets have measure zero. Confluentes Mathematici, Volume 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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