Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: K-property for Maharam extensions of nonsingular Bernoulli and Markov
  shifts   It is shown that each conservative nonsingular Bernoulli shift is either of
type $II_1$ or $III_1$. Moreover, in the latter case the corresponding Maharam
extension of the shift is a $K$-automorphism. This extends earlier results
obtained by Z.~Kosloff for the equilibrial shifts. Nonequilibrial shifts of
type $III_1$ are constructed. We further generalize (partly) the main results
to nonsingular Markov shifts.

12
The categories of this paper are: nucl-th
1
The categories of this paper are: cs
32
The categories of this paper are: atom-ph
30
The categories of this paper are: q-alg
29
The categories of this paper are: funct-an
8
The categories of this paper are: hep-ex
9
The categories of this paper are: nlin
18
The categories of this paper are: econ
10
The categories of this paper are: q-bio
13
The categories of this paper are: quant-ph
36
The categories of this paper are: cmp-lg
7
The categories of this paper are: hep-th
37
The categories of this paper are: supr-con
25
The categories of this paper are: patt-sol
15
The categories of this paper are: nucl-ex
31
The categories of this paper are: ao-sci