A Heredity Property of Sufficiency
HILLE, Jürgen
Tokyo J. of Math., Tome 20 (1997) no. 2, p. 123-127 / Harvested from Project Euclid
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If $(X,\mathscr{A})$ is a measurable space, $(\mathscr{P}_n)_{n\in\mathbf{N}}$ is an increasing sequence of nonempty sets $\mathscr{P}_n$ of probability measures and $\mathscr{B}_n$ is a sub-$\sigma$-field of $\mathscr{A}$ which is sufficient for the statistical experiment $(X,\mathscr{A},\mathscr{P}_n)$, $n\in\mathbf{N}$, then the terminal $\sigma$-field of the sequence $(\mathscr{B}_n)_{n\in\mathbf{N}}$ contains a $\sigma$-field which is sufficient for $\bigcup_{n\in\mathbf{N}}\mathscr{P}_n$.
Publié le : 1997-06-15
Classification:  
@article{1270042404,
     author = {HILLE, J\"urgen},
     title = {A Heredity Property of Sufficiency},
     journal = {Tokyo J. of Math.},
     volume = {20},
     number = {2},
     year = {1997},
     pages = { 123-127},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1270042404}
}

HILLE, Jürgen. A Heredity Property of Sufficiency. Tokyo J. of Math., Tome 20 (1997) no. 2, pp.  123-127. http://gdmltest.u-ga.fr/item/1270042404/