几乎所有非阿基米德Kakeya集合的测度都为零

Q4 Mathematics

Confluentes Mathematici Pub Date : 2016-08-09 DOI:10.5802/CML.44

X. Caruso

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引用次数: 8

摘要

我们用概率的观点研究局部非阿基米德域上的Kakeya集合:我们在上面的Kakeya集合上定义了一个概率测度，并根据这个测度证明了根据Haar测度，几乎所有的非阿基米德Kakeya集合都是可忽略的。我们还讨论了与非阿基米德的Kakeya猜想的可能关系。

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Almost all non-archimedean Kakeya sets have measure zero

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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来源期刊

Confluentes Mathematici Mathematics-Mathematics (miscellaneous)

CiteScore

0.60

自引率

0.00%

发文量

期刊介绍： Confluentes Mathematici is a mathematical research journal. Since its creation in 2009 by the Institut Camille Jordan UMR 5208 and the Unité de Mathématiques Pures et Appliquées UMR 5669 of the Université de Lyon, it reflects the wish of the mathematical community of Lyon—Saint-Étienne to participate in the new forms of scientific edittion. The journal is electronic only, fully open acces and without author charges. The journal aims to publish high quality mathematical research articles in English, French or German. All domains of Mathematics (pure and applied) and Mathematical Physics will be considered, as well as the History of Mathematics. Confluentes Mathematici also publishes survey articles. Authors are asked to pay particular attention to the expository style of their article, in order to be understood by all the communities concerned.