R. Pyke raised the question of the convergence of series indexed by filtering sets. This paper contains a generalization of an inequality of Marcinkiewicz-Zygmund for a certain class of filtering sets, which gives rise to the theory of series for this type of set.
Publié le : 1977-10-14
Classification:
Filtering sets,
isomorphism,
independent random variables,
characteristic functions,
almost everywhere convergence,
60G50,
60G45
@article{1176995719,
author = {Gabriel, Jean-Pierre},
title = {An Inequality for Sums of Independent Random Variables Indexed by Finite Dimensional Filtering Sets and Its Applications to the Convergence of Series},
journal = {Ann. Probab.},
volume = {5},
number = {6},
year = {1977},
pages = { 779-786},
language = {en},
url = {http://dml.mathdoc.fr/item/1176995719}
}
Gabriel, Jean-Pierre. An Inequality for Sums of Independent Random Variables Indexed by Finite Dimensional Filtering Sets and Its Applications to the Convergence of Series. Ann. Probab., Tome 5 (1977) no. 6, pp. 779-786. http://gdmltest.u-ga.fr/item/1176995719/