We show that the main result of [1] on sufficiency of existence of a majorizing measure for boundedness of a stochastic process can be naturally split in two theorems, each of independent interest. The first is that the existence of a majorizing measure is sufficient for the existence of a sequence of admissible nets (as recently introduced by Talagrand [5]), and the second that the existence of a sequence of admissible nets is sufficient for sample boundedness of a stochastic process with bounded increments.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-1-10,
author = {Witold Bednorz},
title = {On Talagrand's Admissible Net Approach to Majorizing Measures and Boundedness of Stochastic Processes},
journal = {Bulletin of the Polish Academy of Sciences. Mathematics},
volume = {56},
year = {2008},
pages = {83-91},
zbl = {1142.60031},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-1-10}
}
Witold Bednorz. On Talagrand's Admissible Net Approach to Majorizing Measures and Boundedness of Stochastic Processes. Bulletin of the Polish Academy of Sciences. Mathematics, Tome 56 (2008) pp. 83-91. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-ba56-1-10/