Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: A characterization for the boundedness of positive operators in a
  filtered measure space   In terms of Sawyer type checking condition, a complete characterization is
established for which the positive operator in a filtered measure space is
bounded from $L^p(d\mu)$ to $L^q(d\mu)$ with $1<p\le q<\infty$.

5
The categories of this paper are: gr-qc
36
The categories of this paper are: cmp-lg
16
The categories of this paper are: stat
4
The categories of this paper are: cond-mat
8
The categories of this paper are: hep-ex
18
The categories of this paper are: econ
17
The categories of this paper are: q-fin
14
The categories of this paper are: math-ph
12
The categories of this paper are: nucl-th
28
The categories of this paper are: alg-geom
35
The categories of this paper are: mtrl-th
6
The categories of this paper are: astro-ph
3
The categories of this paper are: physics
27
The categories of this paper are: comp-gas
7
The categories of this paper are: hep-th
24
The categories of this paper are: dg-ga