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Xavier Caruso
Almost all non-archimedean Kakeya sets have measure zero
Confluentes Mathematici, 10 no. 1 (2018), p. 3-40
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Class. Math.: 05B30, 51E20, 60B11, 11K41
Keywords: Kakeya set, discrete valuation fields

Résumé - 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.

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