|Affiliations:||Mathematical Institute of the Serbian Academy of Sciences and Arts||Title:||A mean value theorem for systems of integrals||Journal:||Journal of Mathematical Analysis and Applications||Volume:||342||Issue:||1||First page:||334||Last page:||339||Issue Date:||1-Jun-2008||Rank:||M21||ISSN:||0022-247X||DOI:||10.1016/j.jmaa.2007.12.012||Abstract:||
More than a century ago, G. Kowalewski stated that for each n continuous functions on a compact interval [a, b], there exists an n-point quadrature rule (with respect to Lebesgue measure on [a, b]), which is exact for given functions. Here we generalize this result to continuous functions with an arbitrary positive and finite measure on an arbitrary interval. The proof relies on a new version of Carathéodory's convex hull theorem, that we also prove in the paper. As an application, we give a discrete representation of second order characteristics for a family of continuous functions of a single random variable.
|Keywords:||Carathéodory's convex hull theorem | Correlation | Covariance | Quadrature rules||Publisher:||Elsevier||Project:||Ministry of Science and Environmental Protection of Serbia, project number 144021|
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