Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Dimension for Martingales   A martingale \int H.dZ is defined as having Dimension k if H has rank k
almost surely, almost all t. Dimension can be used as a geometric invariant to
classify and study martingales. We also define general Brownian motions in
higher dimensions.

23
The categories of this paper are: solv-int
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The categories of this paper are: patt-sol
34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
24
The categories of this paper are: dg-ga
3
The categories of this paper are: physics
18
The categories of this paper are: econ
8
The categories of this paper are: hep-ex
15
The categories of this paper are: nucl-ex
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The categories of this paper are: alg-geom
6
The categories of this paper are: astro-ph
1
The categories of this paper are: cs
29
The categories of this paper are: funct-an
32
The categories of this paper are: atom-ph
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The categories of this paper are: ao-sci