Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Nonstandard analysis, fractal properties and Brownian motion   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.

30
The categories of this paper are: q-alg
23
The categories of this paper are: solv-int
11
The categories of this paper are: hep-lat
33
The categories of this paper are: plasm-ph
5
The categories of this paper are: gr-qc
4
The categories of this paper are: cond-mat
28
The categories of this paper are: alg-geom
3
The categories of this paper are: physics
14
The categories of this paper are: math-ph
7
The categories of this paper are: hep-th
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The categories of this paper are: cmp-lg
25
The categories of this paper are: patt-sol
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
27
The categories of this paper are: comp-gas
34
The categories of this paper are: chem-ph