Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Ergodicity and Conservativity of products of infinite transformations
  and their inverses   We construct a class of rank-one infinite measure-preserving transformations
such that for each transformation $T$ in the class, the cartesian product
$T\times T$ of the transformation with itself is ergodic, but the product
$T\times T^{-1}$ of the transformation with its inverse is not ergodic. We also
prove that the product of any rank-one transformation with its inverse is
conservative, while there are infinite measure-preserving conservative ergodic
Markov shifts whose product with their inverse is not conservative.

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The categories of this paper are: stat
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The categories of this paper are: mtrl-th
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The categories of this paper are: econ
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The categories of this paper are: math-ph
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The categories of this paper are: hep-lat
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The categories of this paper are: patt-sol
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The categories of this paper are: q-fin
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The categories of this paper are: plasm-ph
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The categories of this paper are: gr-qc
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The categories of this paper are: nucl-th
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The categories of this paper are: atom-ph
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The categories of this paper are: solv-int
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The categories of this paper are: q-alg
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The categories of this paper are: hep-th
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The categories of this paper are: alg-geom
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The categories of this paper are: eess