Instruct: Identify the main and secondary category of Arxiv papers based on the titles and abstracts
Query: Krieger's finite generator theorem for actions of countable groups I   For an ergodic probability-measure-preserving action $G \curvearrowright (X,
\mu)$ of a countable group $G$, we define the Rokhlin entropy
$h_G^{\mathrm{Rok}}(X, \mu)$ to be the infimum of the Shannon entropies of
countable generating partitions. It is known that for free ergodic actions of
amenable groups this notion coincides with classical Kolmogorov--Sinai entropy.
It is thus natural to view Rokhlin entropy as a close analogue to classical
entropy. Under this analogy we prove that Krieger's finite generator theorem
holds for all countably infinite groups. Specifically, if
$h_G^{\mathrm{Rok}}(X, \mu) < \log(k)$ then there exists a generating partition
consisting of $k$ sets.

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The categories of this paper are: chao-dyn
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The categories of this paper are: plasm-ph
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The categories of this paper are: supr-con
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The categories of this paper are: ao-sci
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The categories of this paper are: q-bio
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The categories of this paper are: cs
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The categories of this paper are: hep-ex
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The categories of this paper are: astro-ph
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The categories of this paper are: atom-ph
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The categories of this paper are: comp-gas
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The categories of this paper are: gr-qc
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The categories of this paper are: physics
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The categories of this paper are: q-alg
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The categories of this paper are: funct-an
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The categories of this paper are: patt-sol
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The categories of this paper are: adap-org