Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A sufficient condition to a regular set of positive measure on RCD
  spaces   In this paper, we study regular sets in metric measure spaces with bounded
Ricci curvature. We prove that the existence of a point in the regular set of
the highest dimension implies the positivity of the measure of such regular
set. Also we define thee dimension of metric measure spaces and prove the lower
semicontinuity of that under the Gromov-Hausdorff convergence.

35
The categories of this paper are: mtrl-th
16
The categories of this paper are: stat
15
The categories of this paper are: nucl-ex
27
The categories of this paper are: comp-gas
17
The categories of this paper are: q-fin
6
The categories of this paper are: astro-ph
31
The categories of this paper are: ao-sci
14
The categories of this paper are: math-ph
22
The categories of this paper are: chao-dyn
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
26
The categories of this paper are: bayes-an
8
The categories of this paper are: hep-ex
11
The categories of this paper are: hep-lat
28
The categories of this paper are: alg-geom
30
The categories of this paper are: q-alg