The Annals of Probability

A Characterization of Orthogonal Transition Kernels

Lutz W. Weis

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Abstract

A transition kernel $\mu = (\mu_y)_{y\in Y}$ between Polish spaces $X$ and $Y$ is completely orthogonal if there is a perfect statistic $\varphi: X \rightarrow Y$ for $\mu$, i.e. the fibers of the Borel map $\varphi$ separate the $\mu_y$. Equivalent properties are: a) orthogonal, finitely additive measures $p, q$ on $Y$ induce orthogonal mixtures $\mu^p, \mu^q$ on $X$; b) the Markov operator defined by $\mu$ is subjective on a certain class of Borel functions.

Article information

Source
Ann. Probab., Volume 12, Number 4 (1984), 1224-1227.

Dates
First available in Project Euclid: 19 April 2007

Permanent link to this document
https://projecteuclid.org/euclid.aop/1176993152

Digital Object Identifier
doi:10.1214/aop/1176993152

Mathematical Reviews number (MathSciNet)
MR757780

Zentralblatt MATH identifier
0563.60006

JSTOR
links.jstor.org

Subjects
Primary: 60A10: Probabilistic measure theory {For ergodic theory, see 28Dxx and 60Fxx}

Keywords
Orthogonal measures perfect statistics Markov operators which are Riesz homomorphisms or have the Maharam property

Citation

Weis, Lutz W. A Characterization of Orthogonal Transition Kernels. Ann. Probab. 12 (1984), no. 4, 1224--1227. doi:10.1214/aop/1176993152. https://projecteuclid.org/euclid.aop/1176993152


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