Nonstandard Hausdorff dimension in $\mathbb{R}^n$ and an application to the Kakeya conjecture in $\mathbb{R}^3$
Classical Analysis and ODEs
2013-08-29 v2
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.
Keywords
Cite
@article{arxiv.1308.5837,
title = {Nonstandard Hausdorff dimension in $\mathbb{R}^n$ and an application to the Kakeya conjecture in $\mathbb{R}^3$},
author = {Paul Potgieter},
journal= {arXiv preprint arXiv:1308.5837},
year = {2013}
}
Comments
This paper has been withdrawn by the author due to a crucial error in section 5