Nonstandard analysis, fractal properties and Brownian motion
Functional Analysis
2010-05-10 v2
Abstract
In this paper I explore a nonstandard formulation of Hausdorff dimension. By considering an adapted form of the counting measure formulation of Lebesgue measure, I prove a nonstandard version of Frostman's lemma and show that Hausdorff dimension can be computed through a counting argument rather than by taking the infimum of a sum of certain covers. This formulation is then applied to obtain a simple proof of the doubling of the dimension of certain sets under a Brownian motion.
Cite
@article{arxiv.math/0701640,
title = {Nonstandard analysis, fractal properties and Brownian motion},
author = {P. Potgieter},
journal= {arXiv preprint arXiv:math/0701640},
year = {2010}
}
Comments
15 pages