Nonstandard analysis, fractal properties and Brownian motion

Details Nonstandard analysis, fractal properties and Brownian motion Nonstandard analysis, fractal properties and Brownian motion

2007-01-23

arxiv.org/abs/math/0701640v2

Mathematics

Functional Analysis

15 pages

Scientific paper

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.

Affiliated with

Also associated with

No associations

Rating

Nonstandard analysis, fractal properties and Brownian motion does not yet have a rating. At this time, there are no reviews or comments for this scientific paper.

If you have personal experience with Nonstandard analysis, fractal properties and Brownian motion, we encourage you to share that experience with our LandOfFree.com community. Your opinion is very important and Nonstandard analysis, fractal properties and Brownian motion will most certainly appreciate the feedback.

Rate now

Comments { 0 }

Profile ID: LFWR-SCP-O-206097