The orbital equivalence of Bernoulli actions and their Sinai factors

Abstract

<p style='text-indent:20px;'>Given a countable amenable group <inline-formula><tex-math id="M1">\begin{document}$ G $\end{document}</tex-math></inline-formula> and <inline-formula><tex-math id="M2">\begin{document}$ \lambda \in (0,1) $\end{document}</tex-math></inline-formula>, we give an elementary construction of a type-Ⅲ<inline-formula><tex-math id="M3">\begin{document}$ _{\lambda} $\end{document}</tex-math></inline-formula> Bernoulli group action. In the case where <inline-formula><tex-math id="M4">\begin{document}$ G $\end{document}</tex-math></inline-formula> is the integers, we show that our nonsingular Bernoulli shifts have independent and identically distributed factors.