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arXiv · 1308.5837

Nonstandard Hausdorff dimension in $\mathbb{R}^n$ and an application to the Kakeya conjecture in $\mathbb{R}^3$

Paul Potgieter
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Abstract

Through the use of a nonstandard version of Frostman's lemma, the notion of Hausdorff dimension is formulated in nonstandard euclidean space of arbitrary dimension. This allows for a nonstandard proof of the Kakeya conjecture in two dimensions, which can then be extended to the three-dimensional case.

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Paul Potgieter. 2013-08-28. Nonstandard Hausdorff dimension in $\mathbb{R}^n$ and an application to the Kakeya conjecture in $\mathbb{R}^3$. https://arxiv.org/abs/1308.5837

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