Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Hausdorff dimension and $\sigma$ finiteness of $p-$harmonic measures in
  space when $p\geq n$   In this paper we study a p harmonic measure, associated with a positive p
harmonic function \hat{u} defined in an open set O, subset of R^n, and
vanishing on a portion \Gamma of boundary of O. If p>n we show that this p
harmonic measure is concentrated on a set of \sigma- finite H^{n-1} measure
while if p=n the same conclusion holds provided \Gamma is uniformly fat in the
sense of n capacity.

18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
9
The categories of this paper are: nlin
37
The categories of this paper are: supr-con
24
The categories of this paper are: dg-ga
35
The categories of this paper are: mtrl-th
5
The categories of this paper are: gr-qc
23
The categories of this paper are: solv-int
6
The categories of this paper are: astro-ph
8
The categories of this paper are: hep-ex
19
The categories of this paper are: eess
22
The categories of this paper are: chao-dyn
3
The categories of this paper are: physics
12
The categories of this paper are: nucl-th
21
The categories of this paper are: adap-org
27
The categories of this paper are: comp-gas