Almost all non-archimedean Kakeya sets have measure zero

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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Contributor : Xavier Caruso <>
Submitted on : Monday, August 8, 2016 - 11:36:21 AM
Last modification on : Thursday, November 15, 2018 - 11:56:41 AM

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Xavier Caruso. Almost all non-archimedean Kakeya sets have measure zero. Confluentes Mathematici, Institut Camille Jordan et Unité de Mathématiques Pures et Appliquées, 2018, 10 (1), pp.3-40. ⟨10.5802/cml.44⟩. ⟨hal-01352498⟩

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