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August, 1981 Selecting Universal Partitions in Ergodic Theory
John C. Kieffer, Maurice Rahe
Ann. Probab. 9(4): 705-709 (August, 1981). DOI: 10.1214/aop/1176994379


Let $\mathscr{P}$ be the set of all $k$-atom measurable partitions of a standard measurable space $(\Omega, \mathscr{F})$, and let $T$ be an isomorphism of $(\Omega, \mathscr{F})$ onto itself. Given $P \in \mathscr{P}$, each probability measure $\mu$ on $\mathscr{F}$ stationary and ergodic with respect to $T$ determines a joint distribution under $\mu$ of the $k$-state stochastic process $(P, T)$. We say that $P$ is universal for a property $S$ (depending on $\mu$) if the distribution of $(P, T)$ satisfies $S$ for all $\mu$. Theorems are given which assure the existence of a universal $P \in \mathscr{P}$.


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John C. Kieffer. Maurice Rahe. "Selecting Universal Partitions in Ergodic Theory." Ann. Probab. 9 (4) 705 - 709, August, 1981.


Published: August, 1981
First available in Project Euclid: 19 April 2007

zbMATH: 0464.60036
MathSciNet: MR624699
Digital Object Identifier: 10.1214/aop/1176994379

Primary: 28A65
Secondary: 60G10 , 94A15

Keywords: $\bar{d}$ distance , Ergodic decomposition , Ornstein isomorphism theorem , partition distance , Sinai Theorem , stationary process

Rights: Copyright © 1981 Institute of Mathematical Statistics

Vol.9 • No. 4 • August, 1981
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