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Grüss’s inequality, its probabilistic interpretation, and a sharper bound. (English) Zbl 1175.26060

The well-known Chebyshev functional from the probabilistic point of view is nothing else that the covariance of two random variables. Then the Grüss inequality estimates this covariance. The classical estimate is improved under some assumptions on the mean values of the involved random variables.

MSC:

26D15 Inequalities for sums, series and integrals
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