Authors: | Janković, Slobodanka Merkle, Milan |
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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