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

preprint2013arXivOpen access

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

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Nonstandard Hausdorff dimension in Rn\mathbb{R}^nRn and an application to the Kakeya conjecture in R3\mathbb{R}^3R3

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