Open Access
November, 1984 A Characterization of Orthogonal Transition Kernels
Lutz W. Weis
Ann. Probab. 12(4): 1224-1227 (November, 1984). DOI: 10.1214/aop/1176993152


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.


Download Citation

Lutz W. Weis. "A Characterization of Orthogonal Transition Kernels." Ann. Probab. 12 (4) 1224 - 1227, November, 1984.


Published: November, 1984
First available in Project Euclid: 19 April 2007

zbMATH: 0563.60006
MathSciNet: MR757780
Digital Object Identifier: 10.1214/aop/1176993152

Primary: 60A10

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

Rights: Copyright © 1984 Institute of Mathematical Statistics

Vol.12 • No. 4 • November, 1984
Back to Top