A Generalization of Holder's Inequality and Some Probability Inequalities

The main result of this article is a generalization of the generalized Holder inequality for functions or random variables defined on lowerdimensional 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 e N. 1. Introduction. We first recall the generalized Holder inequality in terms of a measure-theoretic approach. Let (fQ, X, /,t) be a measure space and let LP(fb A, But) be the set of p-integrable (1 1 with E i lp-1= 1 and let f;ELp~(fVf ,), jM=1,...,m.