A mean value theorem for systems of integrals

详细信息    查看全文

• 作者：Slobodanka Janković ; Milan Merkle
• 关键词：Carathé ; odory's convex hull theorem ; Quadrature rules ; Covariance ; Correlation
• 刊名：Journal of Mathematical Analysis and Applications
• 出版年：2008
• 出版时间：1 June 2008
• 年：2008
• 卷：342
• 期：1
• 页码：334-339
• 全文大小：120 K

文摘

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.