Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Absolutely continuous, invariant measures for dissipative, ergodic
  transformations   We show that a dissipative, ergodic measure preserving transformation of a
sigma-finite, non-atomic measure space always has many non-proportional,
absolutely continuous, invariant measures and is ergodic with respect to each
one of these.

11
The categories of this paper are: hep-lat
22
The categories of this paper are: chao-dyn
25
The categories of this paper are: patt-sol
4
The categories of this paper are: cond-mat
32
The categories of this paper are: atom-ph
31
The categories of this paper are: ao-sci
21
The categories of this paper are: adap-org
9
The categories of this paper are: nlin
16
The categories of this paper are: stat
36
The categories of this paper are: cmp-lg
19
The categories of this paper are: eess
29
The categories of this paper are: funct-an
1
The categories of this paper are: cs
27
The categories of this paper are: comp-gas
35
The categories of this paper are: mtrl-th
15
The categories of this paper are: nucl-ex