Note on the Tightness of the Metric on the Set of Complete Sub $\sigma$-Algebras of a Probability Space
Neveu, J.
Ann. Math. Statist., Tome 43 (1972) no. 6, p. 1369-1371 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
The purpose of this note is to show that the usual metric on the set of complete $\operatorname{sub} \sigma$-algebras of a probability space is very tight; a recent result from E. B. Boylan on equi-convergence of martingales follows and is thereby, we believe, better understood.
Publié le : 1972-08-14
Classification:  
@article{1177692492,
     author = {Neveu, J.},
     title = {Note on the Tightness of the Metric on the Set of Complete Sub $\sigma$-Algebras of a Probability Space},
     journal = {Ann. Math. Statist.},
     volume = {43},
     number = {6},
     year = {1972},
     pages = { 1369-1371},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1177692492}
}

Neveu, J. Note on the Tightness of the Metric on the Set of Complete Sub $\sigma$-Algebras of a Probability Space. Ann. Math. Statist., Tome 43 (1972) no. 6, pp.  1369-1371. http://gdmltest.u-ga.fr/item/1177692492/