There are no Borel SPLIFs

Blackwell, D.

Blackwell, D.

Ann. Probab., Tome 8 (1980) no. 6, p. 1189-1190 / Harvested from Project Euclid

Résumé

There is no Borel function $f$, defined for all infinite sequences of 0's and 1's, such that for every sequence $X$ of 0-1 random variables that converges in probability to a constant $c$, we have $f(x) = c$ a.s.

Publié le : 1980-12-14
Classification: Convergence in probability, Borel function, 28A20, 28A05

@article{1176994581,
     author = {Blackwell, D.},
     title = {There are no Borel SPLIFs},
     journal = {Ann. Probab.},
     volume = {8},
     number = {6},
     year = {1980},
     pages = { 1189-1190},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176994581}
}

Blackwell, D. There are no Borel SPLIFs. Ann. Probab., Tome 8 (1980) no. 6, pp.  1189-1190. http://gdmltest.u-ga.fr/item/1176994581/