The main result of this article is a generalization of the generalized Holder inequality for functions or random variables defined on lower-dimensional subspaces of $n$-dimensional product spaces. It will be seen that various other inequalities are included in this approach. For example, it allows the calculation of upper bounds for the product measure of $n$-dimensional sets with the help of product measures of lower-dimensional marginal sets. Furthermore, it yields an interesting inequality for various cumulative distribution functions depending on a parameter $n \in \mathbb{N}$.
Publié le : 1992-10-14
Classification:
Generalized Holder inequality,
Gagliardo inequality,
Loomis-Whitney inequality,
range inequality,
product measure,
distribution function,
order statistics,
60E15,
26D15,
62G30,
28A35
@article{1176989534,
author = {Finner, Helmut},
title = {A Generalization of Holder's Inequality and Some Probability Inequalities},
journal = {Ann. Probab.},
volume = {20},
number = {4},
year = {1992},
pages = { 1893-1901},
language = {en},
url = {http://dml.mathdoc.fr/item/1176989534}
}
Finner, Helmut. A Generalization of Holder's Inequality and Some Probability Inequalities. Ann. Probab., Tome 20 (1992) no. 4, pp. 1893-1901. http://gdmltest.u-ga.fr/item/1176989534/