Riesz theorem for positive multilinear functions (Q1929798)
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scientific article; zbMATH DE number 6123766
| Language | Label | Description | Also known as |
|---|---|---|---|
| English | Riesz theorem for positive multilinear functions |
scientific article; zbMATH DE number 6123766 |
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Riesz theorem for positive multilinear functions (English)
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9 January 2013
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The Riesz theorem is a classical result of functional analysis, which states that an arbitrary real-valued continuous linear functional in the space of all continuous real functions on a compact Hausdorff space can be represented by an integral [\textit{F. Riesz}, C. R. 149, 974--977 (1910; JFM 40.0388.03)]. The author extends this result to continuous multilinear functionals on the Cartesian product of a finite number of spaces of all continuous real functions on compact Hausdorff spaces (Theorem 1).
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Riesz theorem
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multilinear function
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multilinear functional
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real-valued Borel measure
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