Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Conditionally atomless extensions of sigma algebras   We give two equivalent definitions of sigma algebras that are atomless
conditionally to a smaller sigma algebra.

34
The categories of this paper are: chem-ph
14
The categories of this paper are: math-ph
30
The categories of this paper are: q-alg
5
The categories of this paper are: gr-qc
20
The categories of this paper are: acc-phys
27
The categories of this paper are: comp-gas
4
The categories of this paper are: cond-mat
33
The categories of this paper are: plasm-ph
10
The categories of this paper are: q-bio
37
The categories of this paper are: supr-con
29
The categories of this paper are: funct-an
7
The categories of this paper are: hep-th
15
The categories of this paper are: nucl-ex
35
The categories of this paper are: mtrl-th
18
The categories of this paper are: econ
28
The categories of this paper are: alg-geom