%0 Journal Article
%T Nonstandard Hausdorff dimension in $\mathbb{R}^n$ and an application to the Kakeya conjecture in $\mathbb{R}^3$
%A Paul Potgieter
%J Mathematics
%D 2013
%I arXiv
%X 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.
%U http://arxiv.org/abs/1308.5837v2