## A generalization of Hölder’s inequality and some probability inequalities.(English)Zbl 0761.60013

Summary: The main result of this article is a generalization of the generalized Hölder 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 $$n\in\mathbb{N}$$.

### MSC:

 60E15 Inequalities; stochastic orderings 26D15 Inequalities for sums, series and integrals 62G30 Order statistics; empirical distribution functions 28A35 Measures and integrals in product spaces
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