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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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