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- W2804063929 abstract "<p style='text-indent:20px;'>We prove that if <inline-formula><tex-math id=M1>begin{document}$ G $end{document}</tex-math></inline-formula> is a countably infinite group and <inline-formula><tex-math id=M2>begin{document}$ (L, lambda) $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=M3>begin{document}$ (K, kappa) $end{document}</tex-math></inline-formula> are probability spaces having equal Shannon entropy, then the Bernoulli shifts <inline-formula><tex-math id=M4>begin{document}$ G curvearrowright (L^G, lambda^G) $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=M5>begin{document}$ G curvearrowright (K^G, kappa^G) $end{document}</tex-math></inline-formula> are isomorphic. This extends Ornstein's famous isomorphism theorem to all countably infinite groups. Our proof builds on a slightly weaker theorem by Lewis Bowen in 2011 that required both <inline-formula><tex-math id=M6>begin{document}$ lambda $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=M7>begin{document}$ kappa $end{document}</tex-math></inline-formula> have at least <inline-formula><tex-math id=M8>begin{document}$ 3 $end{document}</tex-math></inline-formula> points in their support. We furthermore produce finitary isomorphisms in the case where both <inline-formula><tex-math id=M9>begin{document}$ L $end{document}</tex-math></inline-formula> and <inline-formula><tex-math id=M10>begin{document}$ K $end{document}</tex-math></inline-formula> are finite.</p>" @default.
- W2804063929 created "2018-06-01" @default.
- W2804063929 creator A5072591640 @default.
- W2804063929 date "2022-01-01" @default.
- W2804063929 modified "2023-10-14" @default.
- W2804063929 title "Bernoulli shifts with bases of equal entropy are isomorphic" @default.
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- W2804063929 doi "https://doi.org/10.3934/jmd.2022011" @default.
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