A GENERALIZATION OF HOLDERS 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 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 is-an-element-of N.