A Characterization of Orthogonal Transition Kernels
Weis, Lutz W.
Ann. Probab., Tome 12 (1984) no. 4, p. 1224-1227 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
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.
Publié le : 1984-11-14
Classification:  Orthogonal measures,  perfect statistics,  Markov operators which are Riesz homomorphisms or have the Maharam property,  60A10 
@article{1176993152,
     author = {Weis, Lutz W.},
     title = {A Characterization of Orthogonal Transition Kernels},
     journal = {Ann. Probab.},
     volume = {12},
     number = {4},
     year = {1984},
     pages = { 1224-1227},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176993152}
}

Weis, Lutz W. A Characterization of Orthogonal Transition Kernels. Ann. Probab., Tome 12 (1984) no. 4, pp.  1224-1227. http://gdmltest.u-ga.fr/item/1176993152/