Amarts Indexed by Directed Sets
Astbury, Kenneth A.
Ann. Probab., Tome 6 (1978) no. 6, p. 267-278 / Harvested from Project Euclid
Text on Project Euclid
PDF
Alt PDF
We prove that an amart indexed by a directed set decomposes into a martingale and an amart which converges to zero in $L_1$ norm. The main theorem asserts that the underlying family of $\sigma$-algebras satisfies the Vitali condition if and only if every $L_1$ bounded amart essentially converges.
Publié le : 1978-04-14
Classification:  Amart,  martingale,  potential,  directed set,  essential convergence,  Vitali condition,  60F15,  60G40,  60G45,  60G99,  46G10 
@article{1176995572,
     author = {Astbury, Kenneth A.},
     title = {Amarts Indexed by Directed Sets},
     journal = {Ann. Probab.},
     volume = {6},
     number = {6},
     year = {1978},
     pages = { 267-278},
     language = {en},
     url = {http://dml.mathdoc.fr/item/1176995572}
}

Astbury, Kenneth A. Amarts Indexed by Directed Sets. Ann. Probab., Tome 6 (1978) no. 6, pp.  267-278. http://gdmltest.u-ga.fr/item/1176995572/